Where does the y-axis intersect the line that passes through A(-3,-2), B(2,8) ?
You need to find the equation of the line that passes through the indicated points, such that:
`y - y_A = m_(AB)(x - x_A)`
You need to evaluate the slope `m_(AB)` using the following formula, such that:
`m_(AB) = (y_B - y_A)/(x_B - x_A)`
`m_(AB) = (8 + 2)/(2 + 3) => m_(AB) = 10/5 => m_(AB) = 2`
Replacing `2` for `m_(AB) = 2` , `-3` for `x_A` , `-2` for `y_A, ` in equation of the line, yields:
`y + 2 = 2(x + 3) => y + 2 = 2x + 6 => y = 2x + 6 -2 => y = 2x + 4`
The line that passes through the points `A,B` has the equation `y = 2x + 4` and it intersects `y` axis at `x = 0` , such that:
`y = 2*0 + 4 => y = 4`
Hence, evaluating the point where the line `AB` intersects y axis, yields `(0,4)` .