How to find x or y intercept - ACT Math
Card 0 of 144
What is the 
of the following equation: 
?
What is the
The y-intercept is the constant at the end of the equation. Thus for our equation the y-intercept is 7
The y-intercept is the constant at the end of the equation. Thus for our equation the y-intercept is 7
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In the standard (x, y) coordinate plane, a circle has the equation 
. At what points does the circle intersect the x-axis?
In the standard (x, y) coordinate plane, a circle has the equation
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.
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.
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What is the y-intercept of a line that passes through the point 
with slope of 
?
What is the y-intercept of a line that passes through the point
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).
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).
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Given the linear equation below, what are the x- and y-intercepts_,_ respectively?
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 
.
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
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What are the y and x intercepts of the given equation, respectively?
y = 2x – 2
What are the y and x intercepts of the given equation, respectively?
y = 2x – 2
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)
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)
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What is the x-intercept of the following line?
y = –3_x_ + 12
What is the x-intercept of the following line?
y = –3_x_ + 12
The x-intercept occurs when the y-coordinate = 0.
y = –3_x_ + 12
0 = –3_x_ + 12
3_x_ = 12
x = 12/3 = 4
The x-intercept occurs when the y-coordinate = 0.
y = –3_x_ + 12
0 = –3_x_ + 12
3_x_ = 12
x = 12/3 = 4
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What is the x-coordinate of the point in the standard (x,y) coordinate plane at which the two lines y=4x+8 and y=3x-7 intersect?
What is the x-coordinate of the point in the standard (x,y) coordinate plane at which the two lines y=4x+8 and y=3x-7 intersect?
4x+8=3x-7
x+8=-7
x=-15
4x+8=3x-7
x+8=-7
x=-15
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At what point do the lines y=\frac{1}{4}$x+7 and y=4x + 7 intersect?
At what point do the lines y=\frac{1}{4}$x+7 and y=4x + 7 intersect?
Short way:
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:
y=\frac{1}{4}$x+7
y-7 = $\frac{1}{4}$x
x = 4y - 28
Plug this into y=-4x+7
y=-4(4y-28)+7
y=-16y+112+7
17y=119
y=7
Find x
x=4(7)-28=0
Short way:
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:
y=\frac{1}{4}$x+7
y-7 = $\frac{1}{4}$x
x = 4y - 28
Plug this into y=-4x+7
y=-4(4y-28)+7
y=-16y+112+7
17y=119
y=7
Find x
x=4(7)-28=0
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What is the sum of the x-intercepts of 
?
What is the sum of the x-intercepts of
To find the x-intercepts of an equation, you can set its y value equal to zero. Thus, you get for our equation:
Now, factor out all common factors:
From this, you can further factor:
Thus, the x-intercepts of our equation are 
,
, and 
. The sum of these values is 
.
To find the x-intercepts of an equation, you can set its y value equal to zero. Thus, you get for our equation:
Now, factor out all common factors:
From this, you can further factor:
Thus, the x-intercepts of our equation are
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What is the 
-intercept of the line in the standard 
coordinate plane that goes through the points 
and 
?
What is the
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.
The answer is
The slope of the line is determined by calculating the change in
The point-slope form of the equation for the line is then
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What are the 
and 
-intercepts of the line defined by the equation:
What are the
To find the intercepts of a line, we must set the 
and 
values equal to zero and then solve.
To find the intercepts of a line, we must set the
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Find the 
-intercept(s) for the following equation:
Find the
To find the 
intercepts, 
is set equal to 
. This yields:
And finally 
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 
.
To find the
And finally
It is important to realize that both
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What is the largest x-intercept of 
?
What is the largest x-intercept of
To find the x-intercepts of an equation, you can just set the y value of the equation equal to zero. Thus you get, for our data:
Now, you can divide everything by 
to simplify your equation:
Luckily, this is an easy equation to factor:
Based on this, you know that the two intercepts must be where 
and 
. Thus, the largest intercept is 
.
To find the x-intercepts of an equation, you can just set the y value of the equation equal to zero. Thus you get, for our data:
Now, you can divide everything by
Luckily, this is an easy equation to factor:
Based on this, you know that the two intercepts must be where
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What is the 
-intercept of the following linear equation:
?
Give your answer as an ordered pair.
What is the
Give your answer as an ordered pair.
The x-intercept is the value of the linear equation with y = 0 (this means the line will be on the x-axis when y is zero).
Thus we plug 0 in for y and solve for x.
.
Now put it in an ordered pair, remember y = 0:
The x-intercept is the value of the linear equation with y = 0 (this means the line will be on the x-axis when y is zero).
Thus we plug 0 in for y and solve for x.
Now put it in an ordered pair, remember y = 0:
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What is the 
and 
intercepts of the linear equation given by:
?
What is the
To find the 
and 
intercept of a linear equation, find the points where 
and 
are equal to zero.
To do this, plug in zero for either variable and then solve for the other.
this yields:
To find the
To do this, plug in zero for either variable and then solve for the other.
this yields:
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What is the 
and 
intercepts of the following linear equation:
What is the
To find the 
and 
intercepts of an equation, set each variable to zero (one at a time) and solve for the other variable.
Next, set 
to zero:
Now put these two sets of points into two ordered pairs:
To find the
Next, set
Now put these two sets of points into two ordered pairs:
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What is the of the following equation: ?
What is the
The y-intercept is the constant at the end of the equation. Thus for our equation the y-intercept is 7
The y-intercept is the constant at the end of the equation. Thus for our equation the y-intercept is 7
Compare your answer with the correct one above
In the standard (x, y) coordinate plane, a circle has the equation . At what points does the circle intersect the x-axis?
In the standard (x, y) coordinate plane, a circle has the equation
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.
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.
Compare your answer with the correct one above
What is the y-intercept of a line that passes through the point with slope of ?
What is the y-intercept of a line that passes through the point
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).
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).
Compare your answer with the correct one above
Given the linear equation below, what are the x- and y-intercepts_,_ respectively?
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 .
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
Compare your answer with the correct one above