Question

Use the given conditions to write an equation in slope-intercept form passing through (-2, 0) & (0, 2).

a)y = x + 2
b)y = -x + 2
c)y = 2x
d)y = -2x + 2

Answer 1

To find the equation in slope-intercept form with points (-2, 0) and (0, 2), the slope is calculated as 1, and the y-intercept is 2, yielding the equation y = x + 2.

Step-by-step explanation:

To write an equation in slope-intercept form, y = mx + b, where m is the slope and b is the y-intercept, we first need to determine the slope using the points (-2, 0) and (0, 2). The slope (m) is the rise over the run, which is calculated as:

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

The y-intercept (b) can be found by using one of the given points. Using the point (0, 2), where x=0, the y-intercept is immediately given as 2. Thus, the equation of the line is:

y = 1x + 2, which simplifies to y = x + 2.

This corresponds to answer choice (a) y = x + 2.