Question

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

Answer 1

You have 2 points: (-3,0) and (0,4) solve the equation:
(y-y1)=slope*(x-x1)
(y-0)=((4-0)/(0--3))*(x--3)
y=(4/3)*(x+3) or y=4x/3+4

Answer 2

`y=(4)/(3)x+4`

Explanation:

The general form of the slope-intercept equation is:

`y = mx + b`

where
`m` is the slope of the line, and
`b` is the intercept (the point at which the line crosses the y-axis).

In this case we can see by the graph that the intercept is at 4, so
`b = 4`.

And to find the slope, we need to find two points
`(x_(1), y_(1))` and
`(x_(2), y_(2))` of the graph, I will take the points
`(-3,0)` and
`(0,4)`, so:

`x_(1)=-3\\y_(1)=0\\x_(2)=0\\y_(2)=4\\`

And with this data we calculate the slope as follows:

`m=(y_(2)-y_(1))/(x_(2)-x_(2))`

`m=(4-0)/(0-(-3))`

`m=(4)/(3)`

And finally, we substitute the values of
`m` and
`b` in the slope-intercept equation:

`y = mx + b`

`y=(4)/(3)x+4`