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Example Questions
Example Question #1 : How To Graph A Line
A line graphed on the coordinate plane below.
Give the equation of the line in slope intercept form.
The slope of the line is
and the y-intercept is .The equation of the line is
.Example Question #2 : Graphing
Give the equation of the curve.
None of the other answers
This is the parent graph of . Since the graph in question is negative, then we flip the quadrants in which it will approach infinity. So the graph of will start in quadrant 2 and end in 4.
Example Question #4 : How To Graph A Line
The equation
represents a line. This line does NOT pass through which of the four quadrants?Cannot be determined
III
II
IV
I
III
Plug in
for to find a point on the line:
Thus,
is a point on the line.Plug in
for to find a second point on the line:
is another point on the line.
Now we know that the line passes through the points
and .A quick sketch of the two points reveals that the line passes through all but the third quadrant.
Example Question #1 : Graphing
What is the equation of the line in the graph above?
In order to find the equation of a line in slope-intercept form
, 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 . Therefore, .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
.
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
and . Plug them into the equation, and you get
Plugging in those values for
and in the equation, and you getExample Question #1 : How To Graph A Line
What are the x- and y- intercepts of the equation
?
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
is in slope-intercept ( ) 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
, 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:
The x-interecept is therefore (1/2,0).
Example Question #2 : Graphing
Which of the following could be the equation of the line shown in this graph?
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
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