Question

Identify the correct slope and y intercept of the equation 6x – 3y = 12
and
equation of the line passing through the point (–4, –2) and perpendicular to y = –x + 6

Answer 1

Equation of a line is given by y = mx + c; where m is the slope and c is the y-intercept.
For line 6x - 3y = 12
3y = 6x - 12
y = 6/3 x - 12/3
y = 2x - 4

Therefore, slope is 2.

Answer 2

y = mx + b
m = slope
b = y intercept.

6x - 3y = 12
-3y = -6x + 12
-3y/-3 = -6x/-3 + 12/-3
y = 2x - 4
m = slope = 2
b = y intercept = -4

y = -x + 6
m = -1 ; b = 6

(-4,-2)
Since it is perpendicular to y = -x + 6, the slope of (-4,-2) is the opposite reciprocal of the -1.

m = +1

-2 = 1(-4) + b
-2 = -4 + b
b = -2 + 4
b = 2

y = x + 2  is the equation of the line passing through the point (-4,-2)