Question

Select the three equations that pass through the points (–4, –16) and (5, 2): y + 4 = 2(x – 16) y – 2 = 2(x – 5) y = 2x – 8 y + 16 = 2(x + 4)

Answer 1

B, C, D

Explanation:

You want to identify the equations through the points (–4, –16) and (5, 2).

Slope

The slope of the line is given by the formula ...

m = (y2 -y1)/(x2 -x1)

For the given points, the slope of the line through them is ...

m = (2 -(-16))/(5 -(-4)) = 18/9 = 2

Point-slope equation

The point-slope form of the equation for a line is ...

y -k = m(x -h) . . . . . equation for a line with slope m through point (h, k)

Using the first point and the found slope, the equation is ...

y -(-16) = 2(x -(-4))

y +16 = 2(x +4) . . . . . . . . matches choice D

Using the second point, the equation is ...

y -2 = 2(x -5) . . . . . . . . . . matches choice B

Slope-intercept equation

Writing the second point-slope equation in slope-intercept form, we get ...

y = 2x -10 +2 . . . . . . eliminate parentheses, add 2

y = 2x -8 . . . . . . . . . . . . matches choice C