Question

Find the equation of the line given the two points below:

A(-3, -2)
B(6,-8)
a) y = -2x + 6
b) y = -2x - 6
c) y = 2x + 6
d) y = 2x - 6

Answer 1

To find the equation of a line given two points, use the slope-intercept form of a linear equation. For the given points (-3, -2) and (6, -8), the equation of the line is y = -2x - 8/3.

Step-by-step explanation:

To find the equation of a line given two points, you can use the slope-intercept form of a linear equation: y = mx + b, where m is the slope and b is the y-intercept.

1. First, calculate the slope (m) using the formula: m = (y2 - y1) / (x2 - x1)
2. Next, substitute the slope and one of the given points into the equation and solve for b.
3. Finally, write the equation in slope-intercept form using the values of m and b.

For the given points A(-3, -2) and B(6, -8), the slope is (y2 - y1) / (x2 - x1) = (-8 - (-2)) / (6 - (-3)) = -6 / 9 = -2/3. Plugging in one of the points, such as A(-3, -2), we can solve for b: -2 = (-2/3)(-3) + b. Simplifying gives b = -2/3 - 2 = -8/3. Therefore, the equation of the line is y = (-2/3)x - 8/3, which simplifies to y = -2x - 8/3.