PSAT Math : How to find the equation of a line

Study concepts, example questions & explanations for PSAT Math

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Example Questions

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Example Question #526 : Geometry

 

Possible Answers:

Correct answer:

Explanation:

Equation of line: ,    = slope,  = -intercept

Step 1) Find slope ():  rise/run    

Step 2) Find -intercept ():    

                                                      

                                                      

                                                       

Example Question #527 : Geometry

Whast line goes through the points  and ?

Possible Answers:

Correct answer:

Explanation:

Let P_{1}=(1,3) and P_{2}=(7,5)

The slope is geven by:  m = (y_{2} - y_{1}) \div (x_{2} - x_{1})  so

Then we use the slope-intercept form of an equation;   so

And we convert 

 

to standard form.

Example Question #11 : How To Find The Equation Of A Line

What is the equation of the line that passes through the points (4,7) and (8,10)?

Possible Answers:

Correct answer:

Explanation:

In order to find the equation of the line, we will first need to find the slope between the two points through which it passes. The slope, , of a line that passes through the points and is given by the formula below:

We are given our two points, (4,7) and (8,10), allowing us to calculate the slope.

Next, we can use point slope form to find the equation of a line with this slope that passes through one of the given points. We will use (4,7).

Multiply both sides by four to eliminate the fraction, and simplify by distribution.

Subtract from both sides and add twelve to both sides.

This gives our final answer:

Example Question #11 : How To Find The Equation Of A Line

Which line contains the following ordered pairs:

 and

Possible Answers:

\small y=x+14

\small y=-x+14

\small y=-\frac{1}{4}x+\frac{7}{2}

\small y=\frac{1}{4}x+\frac{7}{2}

Correct answer:

\small y=-\frac{1}{4}x+\frac{7}{2}

Explanation:

First, solve for slope.

\small m=\frac{\Delta y}{\Delta x}=\frac{2-4}{6-(-2)}=\frac{-2}{8}=-\frac{1}{4}

Then, substitute one of the points into the equation y=mx+b.

\small 2=(-\frac{1}{4})(6)+b

\small 2=(-\frac{3}{2})+b

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

This leaves us with the equation \small y=-\frac{1}{4}+\frac{7}{2}

Example Question #21 : Psat Mathematics

Axes

Refer to the above red line. What is its equation in standard form?

Possible Answers:

Correct answer:

Explanation:

First, we need to find the slope of the above line. 

The slope of a line. given two points  can be calculated using the slope formula

Set :

Second, we note that the -intercept is the point .

Therefore, in the slope-intercept form of a line, we can set  and :

 

Since we are looking for standard form - that is,  - we do the following:

 

or 

Example Question #21 : Psat Mathematics

Axes

Refer to the above red line. What is its equation in slope-intercept form?

Possible Answers:

Correct answer:

Explanation:

First, we need to find the slope of the above line. 

The slope of a line. given two points  can be calculated using the slope formula

Set :

Second, we note that the -intercept is the point .

Therefore, in the slope-intercept form of a line, we can set  and :

 

Example Question #23 : Psat Mathematics

Axes

Refer to the above red line. A line is drawn perpendicular to that line, and with the same -intercept. What is the equation of that line in slope-intercept form?

Possible Answers:

Correct answer:

Explanation:

First, we need to find the slope of the above line. 

The slope of a line. given two points  can be calculated using the slope formula

Set :

The slope of a line perpendicular to it has as its slope the opposite of the reciprocal of 3, which is .

Since we want the line to have the same -intercept as the above line, which is the point , we can use the slope-intercept form to help us.  We set 

, and solve for  in:

Substitute for  and  in the slope-intercept form, and the equation is

Example Question #12 : How To Find The Equation Of A Line

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

 

 Sat_math_164_05

 
Possible Answers:

 y = -1/2x + 4

y = x/2 + 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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