Question

What is an equation of the line that passes through the points (-9,0) and (6,-5)

Answer 1

y=-1/3x-3

Explanation:

First, we should find the slope

The equation for slope is
`m=(y_2-y_1)/(x_2-x_1)` where m is the slope and the x's and y's are points on the line.

Plug in points

`m=\frac {0-(-5)}{-9-6}\\m=(5)/(-15) \\m=-(1)/(3)`

Meaning the slope is -1/3

The slope intercept form is y=mx+b where m is the slope and b is the y intercept (so far the equation is y=-1/3x+b)

We can also find b by plugging in a point

For example, let's use point (-9,0)

`y=-(1)/(3) x+b\\0=-(1)/(3) (-9)+b\\0=3+b\\b=-3`

Finally, to check, we can use point (6,-5)

`-5=-(1)/(3) (6)-3\\-5=-2-3\\-5=-5\\True`