Question

Consider the graph below:

What is the equation of the line in slope-intercept form?

Answer 1

`y=(-5)/(4)x+5`

Explanation:

Slope intercept form:
`y=mx+b` where
`m` is the slope and
`b` is the y-intercept (the value of y when the line crosses the y-axis)

1) Find the slope of the line (
`m`)

To do this, we can plug the two given points (0,5) and (4,0) into the slope equation:

`(y_2-y_1)/(x_2-x_1) \\= (0-5)/(4-0)\\= (-5)/(4)`

Therefore, the slope of the line is
`(-5)/(4)`.

2) Find the y-intercept of the line (
`b`)

Recall that the y-intercept is the value of y when the line crosses the y-axis. We don't actually need to perform any calculations because on the graph, we can see that the line crosses the y-axis when y=5.

Therefore, the y-intercept of the line is 5.

Plugging both
`m` and
`b` into
`y=mx+b`, we have a final equation of:

`y=(-5)/(4)x+5`

I hope this helps!