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
the point-slope form of the line is
y+6 = -5(x-2)
which ones (possibly rearranged) match that?
To determine which of the 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, which is y = mx + b, where m represents the slope and b represents the y-intercept.
We can substitute the values of the given point (2, -6) into each equation to see if it satisfies the equation.
a. y + 6 = -5(x - 2)
To check if this equation represents a line passing through (2, -6), we substitute x = 2 and y = -6:
-6 + 6 = -5(2 - 2)
0 = 0
Since the equation is satisfied, it represents a line passing through (2, -6) with a slope of -5.
b. y - 2 = -5(x + 6)
To check if this equation represents a line passing through (2, -6), we substitute x = 2 and y = -6:
-6 - 2 = -5(2 + 6)
-8 = -5(8)
-8 = -40
The equation is not satisfied, so it does not represent a line passing through (2, -6) with a slope of -5.
c. y = -5x + 4
To check if this equation represents a line passing through (2, -6), we substitute x = 2 and y = -6:
-6 = -5(2) + 4
-6 = -10 + 4
-6 = -6
The equation is satisfied, so it represents a line passing through (2, -6) with a slope of -5.
d. y = -5x - 28
To check if this equation represents a line passing through (2, -6), we substitute x = 2 and y = -6:
-6 = -5(2) - 28
-6 = -10 - 28
-6 = -38
The equation is not satisfied, so it does not represent a line passing through (2, -6) with a slope of -5.
From the above analysis, the equations that represent a line with a slope of -5 and passes through (2, -6) are a (y + 6 = -5(x - 2)) and c (y = -5x + 4).