Question

there is a coordinate grid with two lines, line a (blue) and line b (green). line a passes through the origin (0,0) and has a positive slope. line b has a y - intercept at (0, - 3.2) and passes through (4,0), with a right triangle drawn to show the rise and run from (0, - 3.2) to (4,0).

Explanation:

To determine the slope of Line \( b \), we can use the two - point form of the slope formula. The slope \( m \) between two points \((x_1,y_1)\) and \((x_2,y_2)\) is given by \( m=\frac{y_2 - y_1}{x_2 - x_1} \)

Step 1: Identify two points on Line \( b \)

We are given one point \((0, - 3.2)\) (the y - intercept) and we can find another point. From the graph, when \( x = 4\), we can find the corresponding \( y \) - value. Looking at the right - angled triangle, the vertical change from \((0,-3.2)\) to the point \((4,0)\) (since at \( x = 4\), the line crosses the \( x \) - axis)

So we have two points \((x_1,y_1)=(0,-3.2)\) and \((x_2,y_2)=(4,0)\)

Step 2: Calculate the slope

Using the slope formula \( m=\frac{y_2 - y_1}{x_2 - x_1} \)

Substitute \( y_2 = 0\), \( y_1=-3.2\), \( x_2 = 4\) and \( x_1 = 0\) into the formula:

\(m=\frac{0-(-3.2)}{4 - 0}=\frac{3.2}{4}=0.8\)

Answer:

The slope of Line \( b \) is \( 0.8 \)