The linear function \(y=g(x)\) is graphed in the \(x y\)-plane. If \(g(-3)=4\) and \(g(2)=19\), what is the slope of line \(g\) ?

Short Answer

Expert verified
The slope of line g is 3.

Step by step solution

01

Identify the coordinates of the two points

We are given two points on the line, which we can label as point A and point B with their corresponding coordinates: Point A: (-3, 4) Point B: (2, 19)
02

Apply the slope formula

Use the coordinates of the two points identified in Step 1 to find the slope of the line g(x) using the formula: Slope (m) = (y2 - y1) / (x2 - x1)
03

Plug in the coordinates and calculate

Now, let's plug in the coordinates of points A and B into the slope formula: m = (19 - 4) / (2 - (-3)) m = (15) / (5)
04

Find the slope

After calculating the value, we find the slope of the line g(x): m = 15 / 5 m = 3 The slope of line g is 3.

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