Question

Write the equation of the line in fully simplified slope-intercept form.

Answer 1

`y=-(1)/(4) x-6`

Explanation:

The slope-intercept form is
`y=mx+c`, where m is the slope of the line and c is where the line crosses the
`y`-axis.

To calculate
`m` we can use the formula
`m = (dy)/(dx)` where
`dy` is the difference in
`y` between two points and
`dx` is the difference between
`x`.

Information we can get from the graph given:
`c=-6`. Since
`c` is the point at which the line crosses the
`y`-axis.

To find
`m` let's get two points from the graph.

Point 1:
`(4,-7)`

Point 2:
`(8,-8)`

Now use the equation
`m = (dy)/(dx)`.

`m = (-7 - (-8))/(4-8) = -(1)/(4)`.

Now we have
`m` and
`c`, let's put them back into the general equation.

`y=-(1)/(4) x-6`