Question

A line is drawn through the points $(-2, 6)$ and $(-4, -2)$. What is the $y$-coordinate of the point where this line intersects the $y$-axis?

Answer 1

This line intersects the y-axis at
`y = 14`

Explanation:

The equation of a line has the following format:

`y = mx + b`

In which m is the slope and b is the y-intercept(point where the line intersects the y-axis).

To find the slope, we take two points, and the slope is given by the change in y divided by the change in x.

In this question:

Points (-2,6) and (-4,-2). So

Change in y: -2 - 6 = -8

Change in x: -4 -(-2) = -4 + 2 = -2

Slope:
`m = (-8)/(-2) = 4`

So
`y = 4x + b`

Now, we take a point, and find b.

Point (-2,6), which means that when
`x = -2, y = 6`. So

`y = 4x + b`

`6 = 4(-2) + b`

`b = 14`

So this line intersects the y-axis at
`y = 14`