SAT Linear Functions Question 62 | Free SAT Prep | Aniko

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Question 62·Medium·Linear Functions

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A line is shown on the graph.

Which choice gives an equation of the line?

For a line-from-graph equation question, read two lattice points to get the slope using $\frac{\Delta y}{\Delta x}$ , then use $y=mx+b$ with one point to find $b$ . Finally, match your $(m,b)$ to an answer choice; most wrong options come from flipping the slope, missing the negative sign, or using the wrong intercept sign.

Hints

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Pick two clear points

Use two points where the line clearly crosses grid intersections (lattice points).

Slope first

Compute $m=\frac{\Delta y}{\Delta x}$ using those two points.

Then find the intercept

After you have $m$ , plug one point into $y=mx+b$ to solve for $b$ .

Desmos Guide

Enter the two points

In Desmos, type the points $(-1,5)$ and $(3,-1)$ as

(-1,5)
(3,-1)

Graph each answer choice

Enter each equation from the choices on separate lines (for example, y=(-3/2)x+(7/2)).

Check which line matches both points

Look for the equation whose graph passes through both plotted points. The correct choice will contain both points exactly.

Step-by-step Explanation

Read two points from the graph

From the graph, the line passes through the points $(-1,5)$ and $(3,-1)$ .

Find the slope

Compute the slope:

m=\frac{-1-5}{3-(-1)}=\frac{-6}{4}=-\frac{3}{2}

Find the $y$ -intercept

Use $y=mx+b$ with $(-1,5)$ and $m=-\frac{3}{2}$ :

5=\left(-\frac{3}{2}\right)(-1)+b=\frac{3}{2}+b

So,

b=5-\frac{3}{2}=\frac{10}{2}-\frac{3}{2}=\frac{7}{2}

Write the equation

Substitute $m=-\frac{3}{2}$ and $b=\frac{7}{2}$ into $y=mx+b$ to get

y=-\frac{3}{2}x+\frac{7}{2}

Strategy

Hints

Desmos Guide

Step-by-step Explanation

Study Hints

Strategy

Hints

Desmos Guide

Step-by-step Explanation