The graph shows the altitude, , in meters, of a drone seconds after takeoff. The relationship between and is linear. Which choice gives an equation for the line shown in the graph?

Solution available with step-by-step explanation

SAT Linear Functions Question 122 | Free SAT Prep | Aniko

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Question 122·Medium·Linear Functions

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The graph shows the altitude, $y$ , in meters, of a drone $x$ seconds after takeoff. The relationship between $x$ and $y$ is linear.

Which choice gives an equation for the line shown in the graph?

When a graph shows a linear relationship, pick two clear points to compute the slope $m$ . If the graph includes a point where $x=0$ , you can read the $y$ -intercept directly as $b$ and write $y=mx+b$ ; otherwise, substitute a point into $y=mx+b$ to solve for $b$ .

Hints

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Use the labeled points

Use the two labeled points on the line as ordered pairs $(x,y)$ .

Compute the slope

Find $m=\frac{\Delta y}{\Delta x}$ using the two points.

Find the intercept

Because one point has $x=0$ , you can read the $y$ -intercept directly. Then write $y=mx+b$ .

Desmos Guide

Enter the two points

In Desmos, enter the points A=(0,12) and B=(8,44).

Make a line through them

Type y-12 = ((44-12)/(8-0))(x-0) to graph the line through the two points.

Compare to the choices

Rewrite the equation in slope-intercept form (or use the displayed line equation) and select the matching answer choice.

Step-by-step Explanation

Read two points from the graph

From the graph, the line passes through $(0,12)$ and $(8,44)$ .

Find the slope

Compute the slope:

m=\frac{44-12}{8-0}=\frac{32}{8}=4

Write the equation

Since the line passes through $(0,12)$ , the $y$ -intercept is $b=12$ . With $m=4$ , the equation is

y=4x+12

So the correct choice is $y=4x+12$ .

Strategy

Hints

Desmos Guide

Step-by-step Explanation

Study Hints

Strategy

Hints

Desmos Guide

Step-by-step Explanation