algebra word problem

Question

two perpendicular lines pass through the (0, -8).  One of the lines has a slope of -4.  write the equation of both lines in slope-intersept-form.

Answer 1

If two perpendicular lines pass at (0,-8), this is their intersect. Conveniently so, (0, -8) is located on the y-axis, aka our y-intercept. We already have the slope for one of the lines, -4. So one of the equations can be written immediately under the slope intercept form, which is the following

 

y = ax + b

 

In this case, our slope, or a, is -4, and our intercept, or our b, is the y intercept, which is -8. 

 

y = -4x+ (-8) = -4x - 8

 

The second line will have the same intercept, since both lines share a common point, at the y intercept. We can find the slope by a property that slope has if it is perpendicular to another.

If we know slope "a" belongs to the first line, then the slope for the line that is perpendicular to it is -1/a. In order words, the slope of a line perpendicular to another is the negative reciprocal of  its slope.

 

The negative reciprocal of -4 is 1/4. 

 

So the equation for the second line is

 

y = 1/4 * x - 8