Find the slope‐intercept equation of the line with the following properties:Perpendicular to the line x-4y=2; containing the point (5,2).
The slope-intercept form of a line is written as `y=mx+b` where m is the slope and b is the y-intercept. To find this equation, we need the slope of the line and any point on the line. We have the point, it is (5,2). The slope is perpendicular to the line:
`-4y=-x+2` divide by -4
which has slope `1/4` . A line perpendicular to this one has a slope that is the negative reciprocal, which has slope -4.
This means the line we are looking for has slope -4 and goes through the point (5,2).
Sub into the equation of the line:
`2=-4(5)+b` solve for b
This means the equation of the line is `y=-4x+22` .