How to find x or y intercept - SAT Math

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Question

A line has the equation: 2x+4y=8.

What is the x-intercept?

Answer

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.

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Question

Which of the following lines does not intersect the line ?

Answer

Parallel lines never intersect, so you are looking for a line that has the same slope as the one given. The slope of the given line is –4, and the slope of the line in y = –4_x_ + 5 is –4 as well. Since these two lines have equal slopes, they will run parallel and can never intersect.

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Question

If the equation of a line is 4_y_ – x = 48, at what point does that line cross the x-axis?

Answer

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

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Question

Where does the graph of 2x + 3y = 15 cross the x-axis?

Answer

To find the x-intercept, set y=0 and solve for x. This gives an answer of x = 7.5.

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Question

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?

Answer

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 = 154

x = 60/3 = 20

x=20

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Question

Find the y-intercept of .

Answer

To find the y-intercept, set x equal to zero and solve for y.

This gives y = 3(0)2 + 2(0) +7 = 7.

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Question

If these three points are on a single line, what is the formula for the line?

(3,3)

(4,7)

(5,11)

Answer

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

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Question

The slope of a line is 5/8 and the x-intercept is 16. Which of these points is on the line?

Answer

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)

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Question

A line has the equation: x+y=1.

What is the y-intercept?

Answer

x+y=1 can be rearranged into: y=-x+1. Using the point-slope form, we can see that the y-intercept is 1.

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Question

Given the line , what is the sum of the -intercept and the -intercept?

Answer

Intercepts occur when a line crosses the -axis or the -axis. When the line crosses the -axis, then and . When the line crosses the -axis, then and . The intercept points are and . So the -intercept is and the intercept is and the sum is .

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Question

What is the y intercept of the following function of x?

y = 3x

Answer

The answer is 0 because in slope intercept form, y = mx + b; b is the y intercept. In this case b = 0.

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Question

What is the x-intercept of a line with a slope of 5 and y-intercept of 3.5?

Answer

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)

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Question

Determine the y-intercept of the following line:

$\dpi{100} \small 3x+6y=9$

Answer

The y-intercept occurs when $\dpi{100} \small x=0$

$\dpi{100} \small 3x+6y=9$

$\dpi{100} \small 3(0)+6y=9$

$\dpi{100} \small 0+6y=9$

$\dpi{100} \small y = \frac{9}{6}=1.5$

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Question

At what point does the graph $3y-2x=31$ cross the -axis?

Answer

The graph crosses the -axis where $x=0$ . So plugging in and solving yields $\frac{31}{3}$ .

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Question

What are the -intercept(s) of the following line:

Answer

We can factor and set equal to zero to determine the -intercepts.

satisfies this equation.

Therefore our -intercepts are and .

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Question

Find the x-intercepts of $25x^{2}+4y^{2} = 9$ .

Answer

To find the x-intercepts, plug $y=0$ into the equation and solve for $x$ .

$25x^{2} + 4\cdot 0^{2} = 9$

$25x^{2} = 9$

$x^{2} = \frac{9}{25}$

$x = \pm \frac{3}{5}$

Don't forget that there are two solutions, both negative and positive!

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Question

Where does the line given by $y=3(x-4)-9$ intercept the -axis?

Answer

First, put in slope-intercept form.

$y=3x-21$ .

To find the -intercept, set and solve for .

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Question

A line with the exquation $y=x^2+3x+c$ passes through the point . What is the -intercept?

Answer

By plugging in the coordinate, we can figure out that . The -Intercept is when , plugging in 0 for gives us .

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Question

The slope of a line is $m=\frac{4}{3}$ . The line passes through $(2,7)$ . What is the x-intercept?

Answer

The equation for a line is:

$y=mx+b$ , or in this case

$y=\frac{4}{3}x+b$

We can solve for $b$ by plugging in the values given

$7=\frac{4}{3}\times 2+b$

$7=2\frac{2}{3}+b$

$b=7-2\frac{2}{3}=4\frac{1}{3}$

Our line is now

$y=\frac{4}{3}x+4\frac{1}{3}$

Our x-intercept occurs when $\dpi{100} y=0$ , so plugging in and solving for $\dpi{100} x$ :

$\dpi{100} 0=\frac{4}{3}x+4\frac{1}{3}$

$\dpi{100} -\frac{13}{3}=\frac{4}{3}x$

$\dpi{100} x=-\frac{13}{4}$

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Question

What is the value of the -intercept for the line given below?

Answer

The x-intercept is where the line crosses the x-axis. In other words,

This gives:

Subtracting 98 from both sides gives:

Dividing both sides by 14 gives the final answer:

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