Question

a) m =
b) b =
c) y =
(and a coordinate plane graph)

Explanation:

Step1: Identify two points on the line

From the graph, the line passes through \((0, -1)\) (the y - intercept) and \((5, 0)\) (the x - intercept).

Step2: Calculate the slope \(m\)

The formula for slope \(m=\frac{y_2 - y_1}{x_2 - x_1}\). Let \((x_1,y_1)=(0, - 1)\) and \((x_2,y_2)=(5,0)\). Then \(m=\frac{0-(-1)}{5 - 0}=\frac{1}{5}=0.2\).

Step3: Determine the y - intercept \(b\)

The y - intercept is the value of \(y\) when \(x = 0\). From the point \((0,-1)\), we can see that \(b=-1\).

Step4: Write the equation of the line

The slope - intercept form of a line is \(y=mx + b\). Substituting \(m=\frac{1}{5}\) and \(b = - 1\) into the formula, we get \(y=\frac{1}{5}x-1\) or \(y = 0.2x-1\).

Answer:

a) \(m=\frac{1}{5}\) (or \(0.2\))
b) \(b = - 1\)
c) \(y=\frac{1}{5}x-1\) (or \(y = 0.2x-1\))