Question

A line passes through the points (5,10) and (-1,-2). Which points lie on the same line? Select all that apply.

a. (6,11)
b. (-2,-4)
c. (3,6)
d. (4,2)
e. (-4,-8)
f. (0,5)

Answer 1

The equation of the line passing through the points (5, 10) and (-1, -2) is y = 2x. The point (4, 8) lies on the same line.

Step-by-step explanation:

The equation of a line passing through two points, (x1, y1) and (x2, y2), can be found using the slope-intercept form: y = mx + b, where m is the slope and b is the y-intercept.

To find the slope, we can use the formula: m = (y2 - y1) / (x2 - x1).

Using the given points, (5, 10) and (-1, -2), we can calculate the slope as follows:

m = (-2 - 10) / (-1 - 5) = -12 / -6 = 2.

So, the slope of the line passing through these points is 2. Now we can use this slope and one of the given points to find the equation of the line.

Using the point (5, 10) and the slope 2, we can substitute these values into the slope-intercept form: y = mx + b, and solve for b:

10 = 2(5) + b, 10 = 10 + b, 10 - 10 = b, b = 0.

Therefore, the equation of the line passing through the points (5, 10) and (-1, -2) is y = 2x.

To determine which points lie on the same line, we can substitute the x and y values of each point into the equation y = 2x and check if the equation is satisfied.

From the given options, the points that satisfy the equation y = 2x are:

• (4, 8): 8 = 2(4) = 8

So, the point (4, 8) lies on the same line.