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If the equation of a line is 4y – x = 48, at what point does that line cross the x-axis?
Possible Answers:
(0,–12)
(0,12)
(–48,0)
(0,–48)
(48,0)
Explanation:
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
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?
Explanation:
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
If these three points are on a single line, what is the formula for the line?
(3,3)
(4,7)
(5,11)
Possible Answers:
y = 4x - 9
y = 3x - 3
y = 4x + 31
y = 5x + 11
y = 3x - 9
Correct answer:
y = 4x - 9
Explanation:
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
The slope of a line is 5/8 and the x-intercept is 16. Which of these points is on the line?
Possible Answers:
(0,10)
(8,15)
(32,30)
(32,10)
(16, 10)
Explanation:
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)
A line has the equation: x+y=1.
What is the y-intercept?
Explanation:
x+y=1 can be rearranged into: y=-x+1. Using the point-slope form, we can see that the y-intercept is 1.
A line has the equation: 2x+4y=8.
What is the x-intercept?
Explanation:
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.
What is the y intercept of the following function of x?
y = 3x
Explanation:
The answer is 0 because in slope intercept form, y = mx + b; b is the y intercept. In this case b = 0.
What is the x-intercept of a line with a slope of 5 and y-intercept of 3.5?
Possible Answers:
(–3.5, 0)
(3.5, 0)
(0, –0.7)
(–0.7, 0)
(0.7, 0)
Explanation:
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)
Determine the y-intercept of the following line:
Correct answer:
Explanation:
The y-intercept occurs when
At what point does the graph cross the -axis?
Correct answer:
Explanation:
The graph crosses the -axis where . So plugging in and solving yields .
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