Question

What is the equation of this graphed line?

Answer 1

To write this equation in slope-intercept form, y = mx + b, we need to find m and b.

m, the slope, is the distance between the points' corresponding y-value divided by the distance between the points' corresponding x-value.

`m=(y_2-y_1)/(x_2-x_1)\\m=(6+6)/(-7+3)\\m=(12)/(-4)\\m=-\frac{12}4\\m=-\frac13`

b, the y-intercept, is shown as -5, but we can solve for it as well when it is not so easy to tell the value of b. We can solve for b by substituting known solutions of x and y after we find m.

`y=mx+b\\-7=-\frac136+b\\-7=-2+b\\-7+2=-2+2+b\\b=-5`

So,

`y=-\frac13x-5`