The equation of the line in slop intercept form is...

Question

Through (-4,7): perpendicular to x=6

Answer 1

You're got a line perpendicular to x=6, which is vertical. That means the line you're looking for is horizontal, so its slope is zero.

y = mx + b, but with a zero slope you have y = b. Since y is 7 if you want to go through (-4, 7), the line equation has to be y = 7.

Answer 2

Since we know the line is perpendicular to x = 6 (which has an undefined slope, we know that the line therefore, must have a slope that's the negative reciprocal of an undefined slope. The undefined slope is defined as m = n/0 where n can be any number. Thus, the slope of the line must be -0/n = 0. Our equation has a slope of 0. Since we know it passes through the point (-4,7), we can use the point-slope form:

y - 7 = 0(x - (-4))

y - 7 = 0

y = 7

y = 7 is the equation of our line