Question

1. y =

m =
b =
(graph of a line on a coordinate grid with two points marked)

Explanation:

Step1: Identify two points on the line

Let's assume the left point is \((-4, 1)\) and the right point is \((4, 3)\) (by counting the grid squares).

Step2: Calculate the slope \(m\)

The formula for slope \(m\) is \(m=\frac{y_2 - y_1}{x_2 - x_1}\). Substituting the points \((x_1,y_1)=(-4,1)\) and \((x_2,y_2)=(4,3)\):

$$ m=\frac{3 - 1}{4 - (-4)}=\frac{2}{8}=\frac{1}{4} $$

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

Using the slope-intercept form \(y = mx + b\) and one of the points, say \((0, 2)\) (by observing the line crosses the y-axis at \(y = 2\)) or using the point \((-4,1)\):
Substitute \(x=-4\), \(y = 1\), and \(m=\frac{1}{4}\) into \(y=mx + b\):

$$ 1=\frac{1}{4}(-4)+b $$

$$ 1=-1 + b $$

$$ b=2 $$

Step4: Write the equation

Using \(m=\frac{1}{4}\) and \(b = 2\), the equation is \(y=\frac{1}{4}x + 2\).

Answer:

\(y=\frac{1}{4}x + 2\), \(m=\frac{1}{4}\), \(b = 2\)