Graphs - PSAT Math
Card 1 of 30
Identify the vertex of the parabola $y=(x-3)^2+4$.
Identify the vertex of the parabola $y=(x-3)^2+4$.
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$(3,4)$. Vertex form $y=(x-h)^2+k$ has vertex at $(h,k)$.
$(3,4)$. Vertex form $y=(x-h)^2+k$ has vertex at $(h,k)$.
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What is the slope of a line perpendicular to a line with slope $m$ (assume $m\ne 0$)?
What is the slope of a line perpendicular to a line with slope $m$ (assume $m\ne 0$)?
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$-\frac{1}{m}$. Perpendicular slopes multiply to $-1$.
$-\frac{1}{m}$. Perpendicular slopes multiply to $-1$.
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Identify the $y$-intercept of the line $4x-5y=10$ as an ordered pair.
Identify the $y$-intercept of the line $4x-5y=10$ as an ordered pair.
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$(0,-2)$. Set $x=0$: $-5y=10$, so $y=-2$.
$(0,-2)$. Set $x=0$: $-5y=10$, so $y=-2$.
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Identify the slope of the line $3x+2y=8$.
Identify the slope of the line $3x+2y=8$.
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$m=-\frac{3}{2}$. Rewrite as $y=-\frac{3}{2}x+4$ to identify slope.
$m=-\frac{3}{2}$. Rewrite as $y=-\frac{3}{2}x+4$ to identify slope.
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What is the $x$-intercept of the line $y=mx+b$ (as a formula, assuming $m\ne 0$)?
What is the $x$-intercept of the line $y=mx+b$ (as a formula, assuming $m\ne 0$)?
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$x=-\frac{b}{m}$. Set $y=0$ and solve for $x$ to find where line crosses $x$-axis.
$x=-\frac{b}{m}$. Set $y=0$ and solve for $x$ to find where line crosses $x$-axis.
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What is the axis of symmetry of the parabola $y=(x+2)^2-7$?
What is the axis of symmetry of the parabola $y=(x+2)^2-7$?
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$x=-2$. Axis of symmetry is $x=h$ for parabola $y=(x-h)^2+k$.
$x=-2$. Axis of symmetry is $x=h$ for parabola $y=(x-h)^2+k$.
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State the slope-intercept form of a line and identify which value is the $y$-intercept.
State the slope-intercept form of a line and identify which value is the $y$-intercept.
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$y=mx+b$; $y$-intercept is $b$. Standard form where $m$ is slope and line crosses $y$-axis at $(0,b)$.
$y=mx+b$; $y$-intercept is $b$. Standard form where $m$ is slope and line crosses $y$-axis at $(0,b)$.
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State the point-slope form of a line with slope $m$ through $(x_1,y_1)$.
State the point-slope form of a line with slope $m$ through $(x_1,y_1)$.
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$y-y_1=m(x-x_1)$. Expresses a line using a known point and the slope.
$y-y_1=m(x-x_1)$. Expresses a line using a known point and the slope.
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What is the slope of a line parallel to a line with slope $m$?
What is the slope of a line parallel to a line with slope $m$?
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$m$. Parallel lines have identical slopes.
$m$. Parallel lines have identical slopes.
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What are the coordinates of the origin on the coordinate plane?
What are the coordinates of the origin on the coordinate plane?
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$(0,0)$. The origin is where both axes intersect at zero.
$(0,0)$. The origin is where both axes intersect at zero.
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What is the vertex of the parabola $y=(x-2)^2-9$?
What is the vertex of the parabola $y=(x-2)^2-9$?
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$(2,-9)$. Vertex form $y=a(x-h)^2+k$ has vertex at $(h,k)$.
$(2,-9)$. Vertex form $y=a(x-h)^2+k$ has vertex at $(h,k)$.
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Identify whether the relation $x^2+y^2=9$ is a function of $x$ using the vertical line test.
Identify whether the relation $x^2+y^2=9$ is a function of $x$ using the vertical line test.
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Not a function. Circle equation fails vertical line test; some $x$ values have two $y$ values.
Not a function. Circle equation fails vertical line test; some $x$ values have two $y$ values.
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What is the slope of a line passing through $(2,5)$ and $(6,1)$?
What is the slope of a line passing through $(2,5)$ and $(6,1)$?
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$-1$. Using slope formula: $\frac{1-5}{6-2}=\frac{-4}{4}=-1$.
$-1$. Using slope formula: $\frac{1-5}{6-2}=\frac{-4}{4}=-1$.
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What is the slope of a vertical line written as $x=c$?
What is the slope of a vertical line written as $x=c$?
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Undefined. Vertical lines have no run, making slope undefined.
Undefined. Vertical lines have no run, making slope undefined.
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What is the slope of a line parallel to a line with slope $-5$?
What is the slope of a line parallel to a line with slope $-5$?
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$-5$. Parallel lines have identical slopes.
$-5$. Parallel lines have identical slopes.
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What is the slope of a line perpendicular to a line with slope $\frac{2}{3}$?
What is the slope of a line perpendicular to a line with slope $\frac{2}{3}$?
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$-\frac{3}{2}$. Perpendicular slopes multiply to $-1$: $\frac{2}{3}\times(-\frac{3}{2})=-1$.
$-\frac{3}{2}$. Perpendicular slopes multiply to $-1$: $\frac{2}{3}\times(-\frac{3}{2})=-1$.
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What is the point-slope form of a line through $(x_1,y_1)$ with slope $m$?
What is the point-slope form of a line through $(x_1,y_1)$ with slope $m$?
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$y-y_1=m(x-x_1)$. Expresses line using a known point and the slope.
$y-y_1=m(x-x_1)$. Expresses line using a known point and the slope.
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What is the slope of a line parallel to $y=-\frac{5}{2}x+9$?
What is the slope of a line parallel to $y=-\frac{5}{2}x+9$?
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$-\frac{5}{2}$. Parallel lines share the same slope coefficient.
$-\frac{5}{2}$. Parallel lines share the same slope coefficient.
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What is the relationship between slopes of parallel nonvertical lines?
What is the relationship between slopes of parallel nonvertical lines?
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Equal slopes: $m_1=m_2$. Parallel lines never intersect.
Equal slopes: $m_1=m_2$. Parallel lines never intersect.
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What is the slope of the line $2x+3y=12$?
What is the slope of the line $2x+3y=12$?
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$-\frac{2}{3}$. Rewrite as $y=-\frac{2}{3}x+4$ to find slope.
$-\frac{2}{3}$. Rewrite as $y=-\frac{2}{3}x+4$ to find slope.
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Identify the equation of the line through $(1,2)$ and $(3,6)$ in slope-intercept form.
Identify the equation of the line through $(1,2)$ and $(3,6)$ in slope-intercept form.
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$y=2x$. Slope is $\frac{6-2}{3-1}=2$; passes through origin.
$y=2x$. Slope is $\frac{6-2}{3-1}=2$; passes through origin.
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Identify the equation of the line with slope $2$ passing through $(0,-3)$.
Identify the equation of the line with slope $2$ passing through $(0,-3)$.
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$y=2x-3$. Use $y=mx+b$ with $m=2$ and $b=-3$.
$y=2x-3$. Use $y=mx+b$ with $m=2$ and $b=-3$.
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Find the slope of the line through $(2,5)$ and $(6,1)$.
Find the slope of the line through $(2,5)$ and $(6,1)$.
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$m=-1$. Using slope formula: $\frac{1-5}{6-2}=\frac{-4}{4}=-1$.
$m=-1$. Using slope formula: $\frac{1-5}{6-2}=\frac{-4}{4}=-1$.
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Identify the $x$-intercept of the line $2x+3y=12$.
Identify the $x$-intercept of the line $2x+3y=12$.
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$(6,0)$. Set $y=0$: $2x+0=12$, so $x=6$.
$(6,0)$. Set $y=0$: $2x+0=12$, so $x=6$.
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What is the $x$-intercept of a graph in terms of coordinates?
What is the $x$-intercept of a graph in terms of coordinates?
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A point where $y=0$. Graph crosses $x$-axis when height is zero.
A point where $y=0$. Graph crosses $x$-axis when height is zero.
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What is the slope of a vertical line?
What is the slope of a vertical line?
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Undefined. Division by zero (no horizontal change) is undefined.
Undefined. Division by zero (no horizontal change) is undefined.
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What is the slope of a horizontal line?
What is the slope of a horizontal line?
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$0$. No vertical change means zero rise over run.
$0$. No vertical change means zero rise over run.
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What is the equation of a horizontal line passing through $y=b$?
What is the equation of a horizontal line passing through $y=b$?
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$y=b$. Horizontal lines have constant $y$-value for all $x$.
$y=b$. Horizontal lines have constant $y$-value for all $x$.
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What is the equation of a vertical line passing through $x=a$?
What is the equation of a vertical line passing through $x=a$?
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$x=a$. Vertical lines have constant $x$-value for all $y$.
$x=a$. Vertical lines have constant $x$-value for all $y$.
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What is the slope-intercept form of a line with slope $m$ and $y$-intercept $b$?
What is the slope-intercept form of a line with slope $m$ and $y$-intercept $b$?
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$y=mx+b$. $m$ is slope, $b$ is where line crosses $y$-axis.
$y=mx+b$. $m$ is slope, $b$ is where line crosses $y$-axis.
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