A line passes through the points and in the -plane. What is the slope of the line?

Solution available with step-by-step explanation

SAT Linear Equations in Two Variables Question 118 | Free SAT Prep | Aniko

00:00

Question 118·Easy·Linear Equations in Two Variables

0 / 140

A line passes through the points $(2,7)$ and $(6,15)$ in the $xy$ -plane. What is the slope of the line?

Your answer

(Express the answer as an integer)

When a question asks for the slope of a line through two points, immediately write the slope formula $m = (y_2 - y_1)/(x_2 - x_1)$ . Carefully label the coordinates, choose an order for the points, and stick to that order in both the numerator and denominator to avoid sign mistakes. Do the two subtractions, then divide and simplify; keeping the process mechanical and consistent helps you work quickly and avoid common errors like flipping the fraction.

Hints

Click me!

Think about what slope measures

Slope measures how much $y$ changes when $x$ increases by 1 unit. It is change in $y$ divided by change in $x$ .

Use the two points to find changes

Find how much the $y$ -value changes going from $(2,7)$ to $(6,15)$ , and how much the $x$ -value changes over the same move.

Form the ratio correctly

Once you know the change in $y$ and the change in $x$ , put change in $y$ in the numerator and change in $x$ in the denominator, then simplify the fraction.

Desmos Guide

Use Desmos to compute the slope expression

In a Desmos expression line, type (15 - 7) / (6 - 2) and press Enter. The numerical value that Desmos displays is the slope of the line through $(2,7)$ and $(6,15)$ .

Step-by-step Explanation

Recall the slope formula

The slope $m$ of a line that passes through two points $(x_1,y_1)$ and $(x_2,y_2)$ is given by

m = \frac{y_2 - y_1}{x_2 - x_1}

That is, slope equals change in $y$ divided by change in $x$ .

Label the points and substitute

Label the points as follows:

First point $(x_1,y_1) =$ (2,7)$
Second point $(x_2,y_2) =$ (6,15)$

Substitute these into the slope formula:

m = \frac{15 - 7}{6 - 2}

Compute the differences and simplify

Now calculate the numerator and denominator:

$15 - 7 = 8$
$6 - 2 = 4$

So the slope is

m = \frac{8}{4} = 2

Therefore, the slope of the line is $2$ .

Strategy

Hints

Desmos Guide

Step-by-step Explanation

Study Hints

Strategy

Hints

Desmos Guide

Step-by-step Explanation