Question

The equation of line QR is y = negative 1 over 2x + 1. Write an equation of a line perpendicular to line QR in slope-intercept form that contains point (5, 6).

Answer 1

Answer:

$\text{The equation of line with slope 2 and passing through the point (5, 6) is }y=2x-4$

Step-by-step explanation:

Given the equation of line QR is

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

we have to find the equation of a line perpendicular to line QR in slope-intercept form that contains point (5, 6).

The slope-intercept form is

$y=mx+c$

Compare general equation with given equation.

$m=-\frac{1}{2}$

As we know the slope of perpendicular line of negative reciprocal of given line therefore, the slope of perpendicular to line QR is

$m=2$

The equation of line with slope m and passing through the point (x',y') is

$y-y'=m(x-x')$

Therefore, the equation of line with slope 2 and passing through the point (5, 6) is

$y-6=2(x-5)$

$y-6=2x-10$

$y=2x-10+6$

$y=2x-4$

which is required slope-intercept form of line perpendicular to line QR.

Answer 2

Any perpendicular line has a negative reciprocal slope. So your slope would be 2. The. You would have the equation : y=2x+b. You would then replace the coordinate (5,6) with x and y on your line to solve for b. Your equation would be : y=2x-4