All ACT Math Resources
Example Question #1 : How To Find X Or Y Intercept
What are the y and x intercepts of the given equation, respectively?
y = 2x – 2
(0, –2), (2, 0)
(0, 0), (0, 0)
(0, –2), (1, 0)
(0, 2), (2, 0)
(0, –2), (–2, 0)
(0, –2), (1, 0)
The equation is already in slope-intercept form. The y-intercept is (0, –2). Plug in 0 for y and we get the x intercept of (1, 0)
Example Question #2 : How To Find X Or Y Intercept
What is the x-intercept of the following line?
y = –3x + 12
The x-intercept occurs when the y-coordinate = 0.
y = –3x + 12
0 = –3x + 12
3x = 12
x = 12/3 = 4
Example Question #3 : How To Find X Or Y Intercept
What is the -coordinate of the point in the standard coordinate plane at which the two lines and intersect?
Example Question #4 : How To Find X Or Y Intercept
What is the -intercept of the line in the standard coordinate plane that goes through the points and ?
The answer is .
The slope of the line is determined by calculating the change in over the change in .
The point-slope form of the equation for the line is then
. The -intercept is determined by setting and solving for . This simplifies to which shows that is the -interecept.
Example Question #5 : How To Find X Or Y Intercept
What are the and -intercepts of the line defined by the equation:
To find the intercepts of a line, we must set the and values equal to zero and then solve.
Example Question #6 : How To Find X Or Y Intercept
In the standard (x, y) coordinate plane, a circle has the equation . At what points does the circle intersect the x-axis?
The generic equation of a circle is (x - x0)2 + (y - y0)2 = r2, where (x0, y0) are the coordinates of the center and r is the radius.
In this case, the circle is centered at the origin with a radius of 8. Therefore the circle hits all points that are a distance of 8 from the origin, which results in coordinates of (8,0) and (-8,0) on the x-axis.
Example Question #7 : How To Find X Or Y Intercept
What is the y-intercept of a line that passes through the point with slope of ?
Point-slope form follows the format y - y1 = m(x - x1).
Using the given point and slope, we can use this formula to get the equation y - 8 = -2(x + 5).
From here, we can find the y-intercept by setting x equal to zero and solving.
y - 8 = -2(0 + 5)
y - 8 = -2(5) = -10
y = -2
Our y-intercept will be (0,-2).
Example Question #8 : How To Find X Or Y Intercept
Given the linear equation below, what are the x- and y-intercepts, respectively?
To find the x-intercept we will need to plug in zero for the y-value.
The x-intercept will be .
To find the y-intercept we will need to plug in zero for the x-value.
The y-intercept will be .
Example Question #9 : How To Find X Or Y Intercept
At what point do the lines and intersect?
The lines intersect somewhere because they have different slopes. Because they have the same y-intercept, they must intersect at that point.
Long way using substitution:
Plug this into
Example Question #10 : How To Find X Or Y Intercept
Find the -intercept(s) for the following equation:
To find the intercepts, is set equal to . This yields:
It is important to realize that both and must be included because is also equal to . Finally, these are put into their point forms, and .