Answer:
This line intersects the y-axis at [tex]y = 14[/tex]
Step-by-step explanation:
The equation of a line has the following format:
[tex]y = mx + b[/tex]
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: [tex]m = \frac{-8}{-2} = 4[/tex]
So [tex]y = 4x + b[/tex]
Now, we take a point, and find b.
Point (-2,6), which means that when [tex]x = -2, y = 6[/tex]. So
[tex]y = 4x + b[/tex]
[tex]6 = 4(-2) + b[/tex]
[tex]b = 14[/tex]
So this line intersects the y-axis at [tex]y = 14[/tex]
