Question

MCQ Question:

Given two points from a line, (0, 8) and (-4, -4), what is the equation of the line that passes through these points?

A) y = 3x + 8
B) y = -3x - 8
C) y = 8x + 3
D) y = -8x + 3

Answer 1

The equation of the line passing through the points (0, 8) and (-4, -4) can be found by calculating the slope and using the point-slope form, resulting in the equation y = 3x + 8.

Step-by-step explanation:

To find the equation of a line that passes through two points, we can use the formula for the slope (m) which is the change in y over the change in x (rise over run). In this case, the points given are (0, 8) and (-4, -4).

The slope can be calculated as follows:

m = (y2 - y1) / (x2 - x1)
m = (-4 - 8) / (-4 - 0)
m = (-12) / (-4)
m = 3

With the slope known, we can use the point-slope form (y - y1 = m(x - x1)) to find the linear equation for the line. Plugging in one of the points and the slope, we get:

y - 8 = 3(x - 0)
y - 8 = 3x
y = 3x + 8

Thus, the correct answer is A) y = 3x + 8.