A scatterplot shows the relationship between the number of minutes a drone has been flying, , and its altitude in meters, . A straight line is drawn on the scatterplot to model the data. Two points on the line are labeled and . Which equation represents the line drawn on the scatterplot?

Solution available with step-by-step explanation

SAT Two-Variable Data Question 4 | Free SAT Prep | Aniko

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Question 4·Easy·Two-Variable Data: Models and Scatterplots

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A scatterplot shows the relationship between the number of minutes a drone has been flying, $x$ , and its altitude in meters, $y$ . A straight line is drawn on the scatterplot to model the data. Two points on the line are labeled $(2,18)$ and $(6,30)$ .

Which equation represents the line drawn on the scatterplot?

When a line is drawn and two points on that line are labeled, treat it like an exact line problem: compute the slope from the two points, then plug one point into $y=mx+b$ to find $b$ . Finally, select the choice with that slope and intercept.

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Use the two labeled points on the line

Compute the slope using $m=\frac{\Delta y}{\Delta x}$ from $(2,18)$ and $(6,30)$ .

Write the line in slope-intercept form

Use $y=mx+b$ after you know $m$ .

Substitute one labeled point

Plug $(2,18)$ (or $(6,30)$ ) into $y=mx+b$ to solve for $b$ .

Desmos Guide

Plot the two labeled points

In Desmos, enter the points $(2,18)$ and $(6,30)$ .

Find the line through the points

Type y1 ~ m x1 + b in Desmos after entering the points in a table, or compute the slope with $\frac{30-18}{6-2}$ and then solve for $b$ using one point.

Match to an answer choice

Use the slope and intercept you found to identify which equation matches the line.

Step-by-step Explanation

Find the slope from the two labeled points

Using $(2,18)$ and $(6,30)$ ,

m = \frac{30-18}{6-2} = \frac{12}{4} = 3

Use a point to find the intercept and write the equation

Use $y = mx + b$ with $(2,18)$ and $m=3$ :

18 = 3(2) + b \Rightarrow 18 = 6 + b \Rightarrow b = 12

So the equation of the line is $y = 3x + 12$ .

Strategy

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Desmos Guide

Step-by-step Explanation

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Strategy

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Desmos Guide

Step-by-step Explanation