Question

The equation of line t is y = -2x + 9. Perpendicular to line t is line u, which passes through

Answer 1

Answer:

Equation of line u in slope-intercept form is: $\mathbf{y=\frac{1}{2}x+9 }$

Step-by-step explanation:

Equation of line t : y = -2x + 9.

We need to find equation of line u, which is perpendicular to line t and passes through point (-10,4)

The equation must be in slope-intercept form.

The general equation of slope-intercept form is: $y=mx+b$ where m is slope and b is y-intercept

Finding Slope:

If two lines are perpendicular, their slopes are opposite i.e $m=-\frac{1}{m}$

Slope of line t: y=-2x+9 we get m =-2 (Comparing with general form y=mx+b, we get m =-2)

Slope of line u: $\frac{1}{2}$

So, we get Slope of line u: m= $\frac{1}{2}$

Finding y-intercept:

Using slope m= $\frac{1}{2}$ and point(-10,4) we can find y-intercept

$y=mx+b\\4=\frac{1}{2}(-10)+b\\4=-5+b\\b=4+5\\b=9$

Equation of line u:

So, equation of line u, having slope m= $\frac{1}{2}$ and y-intercept b=9, we get:

$y=mx+b\\y=\frac{1}{2}x+9$

So, Equation of line u in slope-intercept form is: $\mathbf{y=\frac{1}{2}x+9 }$