Question

Write an equation in slope-intercept form of the line that passes through the given points (-2,2) and (0,4).

Answer 1

The equation in slope-intercept form for the line passing through the points (-2,2) and (0,4) is y = x + 4.

Step-by-step explanation:

To write an equation in slope-intercept form for the line that passes through the points (-2,2) and (0,4), we first need to determine the slope. The slope (m) is the rise over the run, so with our two points, we calculate the slope as:

m = (y2 - y1) / (x2 - x1) = (4 - 2) / (0 - (-2)) = 2 / 2 = 1.

Now that we have the slope, we can use point-slope form to find the y-intercept (b). Using the point (0, 4):

4 = (1)(0) + b

This simplifies to:

b = 4

So the equation of the line in slope-intercept form is:

y = mx + b

y = 1x + 4 or y = x + 4.