Which of the following equations represent a line that has a slope of –5 and that passes through (2, –6)? Check all of the boxes that apply.
a.y + 6 = –5(x – 2)
b.y – 2 = –5(x + 6)
c.y = –5x + 4
d.y = –5x – 28
Algebra 2
ok? do you know how to do it
a and c
To determine which equations represent a line with a slope of -5 and passes through the point (2, -6), we can use the slope-intercept form of a linear equation: y = mx + b, where m is the slope and b is the y-intercept.
First, substitute the given point (2, -6) into each equation and check if the equation holds true.
a. y + 6 = -5(x - 2)
Substitute x = 2 and y = -6: -6 + 6 = -5(2 - 2)
0 = -5(0)
The equation holds true.
b. y - 2 = -5(x + 6)
Substitute x = 2 and y = -6: -6 - 2 = -5(2 + 6)
-8 = -5(8)
The equation does not hold true.
c. y = -5x + 4
Substitute x = 2 and y = -6: -6 = -5(2) + 4
-6 = -10 + 4
-6 = -6
The equation holds true.
d. y = -5x - 28
Substitute x = 2 and y = -6: -6 = -5(2) - 28
-6 = -10 - 28
-6 = -38
The equation does not hold true.
Therefore, the equations that represent a line with a slope of -5 and passes through the point (2, -6) are:
- y + 6 = -5(x - 2)
- y = -5x + 4