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PSAT Math : How to graph a line

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Example Questions

Example Question #1 : How To Graph A Line

A line graphed on the coordinate plane below. Graph_of_y_-2x_4

Give the equation of the line in slope intercept form.

Possible Answers:

$\dpi{100} \small y=-2x+4$

$\dpi{100} \small y=2x+4$

$\dpi{100} \small y=-2x-4$

$\dpi{100} \small y=-x+4$

$\dpi{100} \small y=2x-4$

Correct answer:

$\dpi{100} \small y=-2x+4$

Explanation:

The slope of the line is $\dpi{100} \small -2$ and the y-intercept is $\dpi{100} \small 4$ .

The equation of the line is $\dpi{100} \small y=-2x+4$ .

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Example Question #2 : How To Graph A Line

Graph_of_y_-x_3

Give the equation of the curve.

Possible Answers:

$\dpi{100} \small y=-x^{3}$

$\dpi{100} \small y=x^{4}$

None of the other answers

$\dpi{100} \small y=-x^{2}$

$\dpi{100} \small y=x^{3}$

Correct answer:

$\dpi{100} \small y=-x^{3}$

Explanation:

Graph_of_x_3 This is the parent graph of $\dpi{100} \small x^{3}$ . Since the graph in question is negative, then we flip the quadrants in which it will approach infinity. So the graph of $\dpi{100} \small y=-x^{3}$ will start in quadrant 2 and end in 4.

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Example Question #2 : How To Graph A Line

The equation 3x + 2y = 6 represents a line. This line does NOT pass through which of the four quadrants?

Possible Answers:

III

Cannot be determined

Correct answer:

III

Explanation:

Plug in for to find a point on the line:

3(0) + 2y = 6

y = 3

Thus, (0,3) is a point on the line.

Plug in for to find a second point on the line:

3x + 2(0) = 6

x = 2

(2,0) is another point on the line.

Now we know that the line passes through the points (2,0) and (0,3) .

A quick sketch of the two points reveals that the line passes through all but the third quadrant.

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Example Question #1 : Graphing

Psat1question

What is the equation of the line in the graph above?

Possible Answers:

y = 2x-1

y = 2x +1

y = x + 2

y=x-1

y = x + 1

Correct answer:

y = 2x-1

Explanation:

In order to find the equation of a line in slope-intercept form $\left( y = mx+b$ , where is the slope and is the y-intercept), one must know or otherwise figure out the slope of the line (its rate of change) and the point at which it intersects the y-axis. By looking at the graph, you can see that the line crosses the y-axis at y=-1 . Therefore, b=-1 .

Slope is the rate of change of a line, which can be calculated by figuring out the change in y divided by the change in x, using the formula

$m = \frac{\Delta y}{\Delta x} = \frac{y_{2}-y_{1}}{x_{2}-x_{1}}$ .

When looking at a graph, you can pick two points on a graph and substitute their x- and y-values into that equation. On this graph, it's easier to choose points like (0,-1) and (1,1) . Plug them into the equation, and you get

$m = \frac{1+1}{1-0} = \frac{2}{1} = 2$

Plugging in those values for and in the equation, and you get y=2x-1

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Example Question #1 : How To Graph A Line

What are the x- and y- intercepts of the equation y = 4x -2 ?

Possible Answers:

$\left ( 4,0\right )\ \textup{and}\ \left ( 0,-2\right )$

$\left ( -2,0\right )\ \textup{and}\ \left ( 0,\frac{1}{2}\right )$

$\left ( \frac{1}{2},0 \right )\textup{and}\left ( 0,-2\right )$

$\left ( -2,0\right )\ \textup{and}\left ( 0,-4\right )$

$\left ( -2,0\right )\ \textup{and}\ \left ( 0,4\right )$

Correct answer:

$\left ( \frac{1}{2},0 \right )\textup{and}\left ( 0,-2\right )$

Explanation:

Answer: (1/2,0) and (0,-2)

Finding the y-intercept: The y-intercept is the point at which the line crosses tye y-axis, meaning that x = 0 and the format of the ordered pair is (0,y) with y being the y-intercept. The equation y=4x-2 is in slope-intercept ( y=mx+b ) form, meaning that the y-intercept, b, is actually given in the equation. b = -2, which means that our y-intercept is -2. The ordered pair for expressing this is (0,-2)

Finding the x-intercept: To find the x-intercept of the equation y=4x-2 , we must find the point where the line of the equation crosses the x-axis. In other words, we must find the point on the line where y is equal to 0, as it is when crossing the x-axis. Therefore, substitute 0 into the equation and solve for x: 0=4x-2

2 = 4x

1/2=x

The x-interecept is therefore (1/2,0).

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Example Question #3 : Graphing

Which of the following could be the equation of the line shown in this graph?

Line

Possible Answers:

$y=-\frac{2}{3}x +1$

$y=\frac{2}{3}x +2$

$y=-\frac{7}{6}x -4$

$y=\frac{4}{3}x -5$

$y=-\frac{5}{7}x -1$

Correct answer:

$y=-\frac{2}{3}x +1$

Explanation:

The line in the diagram has a negative slope and a positive y-intercept. It has a negative slope because the line moves from the upper left to the lower right, and it has a positive y-intercept because the line intercepts the y-axis above zero.

The only answer choice with a negative slope and a positive y-intercept is

$y=-\frac{2}{3}x +1$

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PSAT Math : How to graph a line

Study concepts, example questions & explanations for PSAT Math

All PSAT Math Resources

Example Questions

Example Question #1 : How To Graph A Line

Example Question #2 : How To Graph A Line

Example Question #2 : How To Graph A Line

Example Question #1 : Graphing

Example Question #1 : How To Graph A Line

Example Question #3 : Graphing

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