SAT Math : How to find x or y intercept
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Example Question #1 : How To Find X Or Y Intercept
If the equation of a line is 4y – x = 48, at what point does that line cross the x-axis?
(0,–48)
(0,–12)
(–48,0)
(48,0)
(0,12)
(–48,0)
When the equation crosses the x-axis, y = 0. Plug 0 into the equation for y, and solve for x.
4(0) – x = 48, –x = 48, x = –48
Example Question #2 : How To Find X Or Y Intercept
The slope of a line is equal to -3/4. If that line intersects the y-axis at (0,15), at what point does it intersect the x-axis?
15
5
-20
20
60
20
If the slope of the line m=-3/4, when y=15 and x=0, plug everything into the equation y=mx+b.
Solving for b:
15=(-3/4)*0 + b
b=15
y=-3/4x + 15
To get the x-axis intersect, plug in y=0 and solve for x.
0 = -3/4x + 15
3/4x = 15
3x = 15*4
x = 60/3 = 20
x=20
Example Question #1 : How To Find X Or Y Intercept
If these three points are on a single line, what is the formula for the line?
(3,3)
(4,7)
(5,11)
y = 3x - 3
y = 5x + 11
y = 3x - 9
y = 4x + 31
y = 4x - 9
y = 4x - 9
Formula for a line: y = mx + b
First find slope from two of the points: (3,3) and (4,7)
m = slope = (y2 – y1) / x2 – x1) = (7-3) / (4-3) = 4 / 1 = 4
Solve for b by plugging m and one set of coordinates into the formula for a line:
y = mx + b
11 = 4 * 5 + b
11 = 20 + b
b = -9
y = 4x - 9
Example Question #201 : Coordinate Geometry
The slope of a line is 5/8 and the x-intercept is 16. Which of these points is on the line?
(16, 10)
(32,30)
(32,10)
(8,15)
(0,10)
(32,10)
y = mx + b
x intercept is 16 therefore one coordinate is (16,0)
0 = 5/8 * 16 + b
0 = 10 + b
b = -10
y = 5/8 x – 10
if x = 32
y = 5/8 * 32 – 10 = 20 – 10 = 10
Therefore (32,10)
Example Question #2 : How To Find X Or Y Intercept
A line has the equation: x+y=1.
What is the y-intercept?
1
-1
0
2
0.5
1
x+y=1 can be rearranged into: y=-x+1. Using the point-slope form, we can see that the y-intercept is 1.
Example Question #3 : How To Find X Or Y Intercept
A line has the equation: 2x+4y=8.
What is the x-intercept?
-8
-4
0
4
8
4
To find the x-intercept, rearrange the equation 2x+4y=8 so that x is isolated:
2x=-4y+8
x=-2y+4
Using the point-slope formula, we see that the x-intercept is 4.
Example Question #1 : How To Find X Or Y Intercept
What is the y intercept of the following function of x?
y = 3x
0
–1
3
–3
1
0
The answer is 0 because in slope intercept form, y = mx + b; b is the y intercept. In this case b = 0.
Example Question #2 : How To Find X Or Y Intercept
What is the x-intercept of a line with a slope of 5 and y-intercept of 3.5?
(–0.7, 0)
(0, –0.7)
(–3.5, 0)
(3.5, 0)
(0.7, 0)
(–0.7, 0)
To solve this, first find the equation of our line. The form of the question gives it to us very directly. We can use the slope-intercept form (y = mx + b).
y = 5x + 3.5
The x-intercept is found by setting y = 0, because that will give us the x-value at which the line crosses the x-axis.
0 = 5x + 3.5; –3.5 = 5x; x = –3.5 / 5 or –0.7. The point will be (–0.7, 0)
Example Question #4 : How To Find X Or Y Intercept
Determine the y-intercept of the following line:
The y-intercept occurs when
Example Question #161 : Psat Mathematics
At what point does the graph 
The graph crosses the 
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