Question

Write an equation of the line passing through each pair of points
(-2,-6), (4,6)

Answer 1

To write the equation of a line passing through two points, use the slope-intercept form y = mx + b. Calculate the slope using (y2 - y1) / (x2 - x1), then substitute the coordinates of one point into the equation to solve for the y-intercept.

Step-by-step explanation:

To write the equation of a line passing through two points, we can use the slope-intercept form: y = mx + b.

1. First, we need to find the slope (m) of the line. This can be calculated using the formula: m = (y2 - y1) / (x2 - x1). For the given points (-2,-6) and (4,6), the slope is (6 - (-6)) / (4 - (-2)) = 12 / 6 = 2.
2. Next, we can choose either of the given points and substitute its coordinates into the equation to solve for the y-intercept (b). Let's use the point (-2,-6): -6 = 2(-2) + b. Solving for b, we get b = -2.
3. Finally, we can substitute the values of m and b into the equation to get the final equation: y = 2x - 2.