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SAT Math : How to find the equation of a line

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Example Question #1 : Coordinate Geometry

What is the equation of a line that passes through coordinates $\dpi{100} \small (2,6)$ and $\dpi{100} \small (3,5)$ ?

Possible Answers:

$\dpi{100} \small y=x+7$

$\dpi{100} \small y=-x+8$

$\dpi{100} \small y=2x+4$

$\dpi{100} \small y=2x-4$

$\dpi{100} \small y=3x+2$

Correct answer:

$\dpi{100} \small y=-x+8$

Explanation:

Our first step will be to determing the slope of the line that connects the given points.

$m=\frac{y_2-y_1}{x_2-x_1}=\frac{6-5}{2-3}=\frac{1}{-1}=-1$

Our slope will be . Using slope-intercept form, our equation will be y=(-1)x+b . Use one of the give points in this equation to solve for the y-intercept. We will use $\dpi{100} \small (2,6)$ .

6=(-1)(2)+b

6=-2+b

8=b

Now that we know the y-intercept, we can plug it back into the slope-intercept formula with the slope that we found earlier.

y=(-1)x+8

y=-x+8

This is our final answer.

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Example Question #1441 : Gre Quantitative Reasoning

Which of the following equations does NOT represent a line?

Possible Answers:

5y=10

x-y=10

x+y=10

x=10

x^2+y=10

Correct answer:

x^2+y=10

Explanation:

The answer is x^2+y=10 .

A line can only be represented in the form x=z or y=mx+b , for appropriate constants , , and . A graph must have an equation that can be put into one of these forms to be a line.

x^2+y=10 represents a parabola, not a line. Lines will never contain an x^2 term.

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Example Question #1 : How To Find The Equation Of A Line

Let y = 3x – 6.

At what point does the line above intersect the following:

$2x =\frac{2}{3}y+4$

Possible Answers:

(–5,6)

They do not intersect

They intersect at all points

(0,–1)

(–3,–3)

Correct answer:

They intersect at all points

Explanation:

If we rearrange the second equation it is the same as the first equation. They are the same line.

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Example Question #11 : New Sat Math No Calculator

Find the equation of a line that goes through the points (0,3) , and (-10,4) .

Possible Answers:

y=-10x

$y=-\frac{1}{10}x+3$

y=-13x

y=-10x+3

$y=-\frac{1}{10}x$

Correct answer:

$y=-\frac{1}{10}x+3$

Explanation:

For finding the equation of a line, we will be using point-slope form, which is

y-y_0=m(x-x_0) , where is the slope, and (x_0, y_0) is a point.

$m=\frac{y_2-y_1}{x_2-x_1}=\frac{4-3}{-10-0}=\frac{1}{-10}=-\frac{1}{10}$

We will pick the point (0,3)

$y-3=-\frac{1}{10}(x-0)$

$y=-\frac{1}{10}x+3$

If we picked the point (-10,4)

$y-4=-\frac{1}{10}(x+10)$

$y=-\frac{1}{10}x-1+4$

$y=-\frac{1}{10}x+3$

We get the same result

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Example Question #21 : How To Find The Equation Of A Line

Find the equation of a line that passes through the point (-2,5) , and is parallel to the line y=-3x+4 .

Possible Answers:

y=-3x-3

y=-3x+1

y=-3x-1

y=-3x-10

y=-3x

Correct answer:

y=-3x-1

Explanation:

Since we want a line that is parallel, we will have the same slope as the line (-3) . We can use point slope form to create an equation.

y-y_0=m(x-x_0) , where is the slope and (x_0, y_0) is a point.

y-5=-3(x-(-2))

y-5=-3(x+2)

y-5=-3x-6

y=-3x-1

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Example Question #61 : Other Lines

Find the equation of the line shown in the graph below:

Sat_math_164_05

Possible Answers:

y = x/2 + 4

y = -1/2x + 4

y = -1/2x - 4

y = 2x + 4

Correct answer:

y = x/2 + 4

Explanation:

Based on the graph the y-intercept is 4. So we can eliminate choice y = x/2 - 4.

The graph is rising to the right which means our slope is positive, so we can eliminate choice y = -1/2x + 4.

Based on the line, if we start at (0,4) and go up 1 then 2 to the right we will be back on the line, meaning we have a slope of (1/2).

Using the slope intercept formula we can plug in y= (1/2)x + 4.

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SAT Math : How to find the equation of a line

Study concepts, example questions & explanations for SAT Math

All SAT Math Resources

Example Questions

Example Question #1 : Coordinate Geometry

Example Question #1441 : Gre Quantitative Reasoning

Example Question #1 : How To Find The Equation Of A Line

Example Question #11 : New Sat Math No Calculator

Example Question #21 : How To Find The Equation Of A Line

Example Question #61 : Other Lines

All SAT Math Resources

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