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Undefined control sequence \dpi
Undefined control sequence \dpi
Undefined control sequence \dpi

SAT Math : How to find the equation of a line

Study concepts, example questions & explanations for SAT Math

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Example Questions

Example Question #141 : Lines

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=2x-4

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

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

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

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

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.

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

Our slope will be \displaystyle -1. Using slope-intercept form, our equation will be \displaystyle 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).

\displaystyle 6=(-1)(2)+b

\displaystyle 6=-2+b

\displaystyle 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.

\displaystyle y=(-1)x+8

\displaystyle y=-x+8

This is our final answer.

Example Question #2 : How To Find The Equation Of A Line

Which of the following equations does NOT represent a line?

Possible Answers:

\displaystyle x^2+y=10

\displaystyle x=10

\displaystyle x+y=10

\displaystyle x-y=10

\displaystyle 5y=10

Correct answer:

\displaystyle x^2+y=10

Explanation:

The answer is \displaystyle x^2+y=10.

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

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

Example Question #5 : How To Find The Equation Of A Line

Let y = 3x – 6.

At what point does the line above intersect the following:

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

 

 

Possible Answers:

(0,–1)

(–5,6)

They intersect at all points

They do not intersect

(–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.

Example Question #141 : Coordinate Geometry

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

Possible Answers:

\displaystyle y=-10x

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

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

\displaystyle y=-10x+3

\displaystyle y=-13x

Correct answer:

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

Explanation:

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

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

\displaystyle 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 \displaystyle (0,3)

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

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

If we picked the point \displaystyle (-10,4)

 

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

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

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

We get the same result

Example Question #151 : Coordinate Geometry

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

Possible Answers:

\displaystyle y=-3x-1

\displaystyle y=-3x+1

\displaystyle y=-3x-10

\displaystyle y=-3x

\displaystyle y=-3x-3

Correct answer:

\displaystyle y=-3x-1

Explanation:

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

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

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

\displaystyle y-5=-3(x+2)

\displaystyle y-5=-3x-6

\displaystyle y=-3x-1

Example Question #152 : Coordinate Geometry

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 = 2x + 4

 y = -1/2x + 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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