Line is shown in the -plane. Which choice is the equation of line ?

Solution available with step-by-step explanation

SAT Linear Equations in Two Variables Question 19 | Free SAT Prep | Aniko

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Question 19·Easy·Linear Equations in Two Variables

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Line $t$ is shown in the $xy$ -plane.

Which choice is the equation of line $t$ ?

When a line is given on a graph, pick two clear points on the line (especially labeled ones) to find the slope using $\frac{\Delta y}{\Delta x}$ . Then plug one point into $y=mx+b$ to find $b$ . Finally, match $y=mx+b$ to the choice that has both the correct slope and intercept.

Hints

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Use the labeled points

Identify the two labeled points on line $t$ and use them to compute the slope.

Rise over run

Compute $\frac{\Delta y}{\Delta x}$ using the two points to get the slope $m$ .

Solve for the intercept

Plug one of the points into $y=mx+b$ to find $b$ .

Desmos Guide

Enter the points from the graph

In Desmos, type the points A=(-1,3) and B=(2,9).

Compute the slope

Type m=(9-3)/(2-(-1)) and note the value Desmos gives for $m$ .

Compute the y-intercept

Type b=3-m*(-1) (or use the other point with b=9-m*2) to get $b$ .

Match to an option

Form the equation y=mx+b and compare it to the four answer choices to select the matching equation.

Step-by-step Explanation

Find the slope and intercept from two points

From the graph, line $t$ passes through $(-1,3)$ and $(2,9)$ . The slope is

m=\frac{9-3}{2-(-1)}=\frac{6}{3}=2.

Use $y=mx+b$ with $(-1,3)$ :

3=2(-1)+b \Rightarrow 3=-2+b \Rightarrow b=5.

Write the equation

With $m=2$ and $b=5$ , the equation of the line is $y=2x+5$ .

Strategy

Hints

Desmos Guide

Step-by-step Explanation

Study Hints

Strategy

Hints

Desmos Guide

Step-by-step Explanation