Question

What is the slope-intercept form of the line passing through `(-1, 4)` and `(-4, 2)`?

Answer 1

The line's equation is:
`y = (2/3) x + (14/3)`

Hence the y-axis intercept is 14/3
and the slope is 2/3.

Explanation:

slope = change in y / change in x

For points on the line at: (-1,4) and (-4,2)
change in y = 4 - 2 = 2
change in x = (-1) - (-4) = 3

Therefore:
slope = m = 2/3

The equation for a line is:
y = m x + c
Where c is the y-axis intercept.
Taking the first point, where x= -1 and y=4.
4 = (2/3) (-1) + c
c = 4 + (2/3) = 14/3

The line's equation is:
`y = (2/3) x + (14/3)`