Question

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

the point (-10, 4). What is the equation of line u?
Write the equation in slope-intercept form. Write the numbers in the equation as proper
fractions, improper fractions, or integers.

Answer 1

Equation of line u in slope-intercept form is:
`\mathbf{y=(1)/(2)x+9 }`

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=-(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:
`(1)/(2)`

So, we get Slope of line u: m=
`(1)/(2)`

Finding y-intercept:

Using slope m=
`(1)/(2)` and point(-10,4) we can find y-intercept

`y=mx+b\\4=(1)/(2)(-10)+b\\4=-5+b\\b=4+5\\b=9`

Equation of line u:

So, equation of line u, having slope m=
`(1)/(2)` and y-intercept b=9, we get:

`y=mx+b\\y=(1)/(2)x+9`

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