Question

write an equation of the line below.
your answer

Explanation:

Step1: Identify two points on the line

From the graph, we can see that the line passes through \((0, -1)\) (the y - intercept) and \((2, 7)\).

Step2: Calculate the slope \(m\)

The formula for slope between two points \((x_1,y_1)\) and \((x_2,y_2)\) is \(m=\frac{y_2 - y_1}{x_2 - x_1}\).
Using \((x_1,y_1)=(0, - 1)\) and \((x_2,y_2)=(2,7)\), we have \(m=\frac{7-(-1)}{2 - 0}=\frac{8}{2}=4\).

Step3: Use the slope - intercept form \(y=mx + b\)

The slope - intercept form of a line is \(y = mx + b\), where \(m\) is the slope and \(b\) is the y - intercept.
We know that \(m = 4\) and from the point \((0,-1)\), the y - intercept \(b=-1\).
So the equation of the line is \(y = 4x-1\).

Answer:

\(y = 4x - 1\)