Question

Create the linear equation in the form y=mx+b using the graph where m is the slope, and b is the y intercept. Use the slope equation formula to find the slope, and the y intercept to help.

Answer 1

We will find the linear equation of the graph shown. For doing so, we will find the slope with the formula:

$m=\frac{y_2-y_1}{x_2-x_1}$

Where (x₁, y₁) and (x₂, y₂) are the coordinates of two points of the line.

In this line, we see that the graph passes through the points:

$(6,0)\text{ and }(0,3)$

This gives us the y-intercept, as the function passes for y=3, when x=0. The slope is given by:

$m=\frac{3-0}{0-6}=\frac{3}{-6}=-\frac{1}{2}$

Hence, the linear equation of the function shown is:

$y=-\frac{1}{2}x+3$