Where does the y-axis intersect the line that passes through A(-3,-2), B(2,8) ?

Expert Answers

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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)` .

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