Question

What is the equation, in slope-intercept form, of the line that is perpendicular to the line

Answer 1

Answer:

$y=\frac{1}{2} x-1$

Step-by-step explanation:

The initial line is given in "point-slope form" ($y-y_0=m(x-x_0)$ therefore we can easily extract from it the slope, and obtain from it what should be the slope of a line perpendicular to it:

Given the expression: $y-4=-2(x-6)$

we understand that the slope is "-2", and the point through which the line passes is the point (6,4) on the plane. We are concerned about the slope, since a line perpendicular to the given line must have a slope that corresponds to the "opposite of the reciprocal" of the original slope.

The opposite of "-2" is "2", and the reciprocal of this is "1/2".

Therefore the slope of the perpendicular line must be "1/2".

Now we can build the equation of the line perpendicular line through the point (-2,-2) by using again the "point-slope form":

$y-y_0=m(x-x_0)\\y-(-2)=\frac{1}{2} (x-(-2))\\y+2=\frac{1}{2} (x+2)$

Solving for y in this last expression we express the line in slope_y-intercept form:

$y+2=\frac{1}{2} (x+2)\\y+2=\frac{1}{2} x+1\\y=\frac{1}{2} x+1-2\\y=\frac{1}{2} x-1$