Question

there is a coordinate grid with two lines, line a (blue) passing through the origin and line b (green) with a point (0, -3.2) marked. there is also a label line b in a box on the right side.

Explanation:

Assuming we need to find the equation of Line \( b \) (since it's a common problem with such a graph), let's proceed:

Step1: Identify slope formula

The slope \( m \) of a line through two points \((x_1,y_1)\) and \((x_2,y_2)\) is \( m = \frac{y_2 - y_1}{x_2 - x_1} \). Line \( b \) passes through \((0, -3.2)\) (y-intercept) and \((4, 0)\) (from the graph, it crosses the x-axis at \( x = 4 \), \( y = 0 \)).

Step2: Calculate slope

Using \((0, -3.2)\) as \((x_1,y_1)\) and \((4, 0)\) as \((x_2,y_2)\):
\( m = \frac{0 - (-3.2)}{4 - 0} = \frac{3.2}{4} = 0.8 \) (or \( \frac{4}{5} \) if we consider exact fractions, but 0.8 is decimal).

Step3: Write the equation

The slope-intercept form is \( y = mx + b \), where \( b \) (the y-intercept) is \(-3.2\) (from the point \((0, -3.2)\)) and \( m = 0.8 \). So the equation is \( y = 0.8x - 3.2 \).

Answer:

The equation of Line \( b \) is \( \boldsymbol{y = 0.8x - 3.2} \) (or \( y = \frac{4}{5}x - \frac{16}{5} \) in fractional form).