Help!!!!!!!!!!!!!!!!!!!

Question

The equation of line t is y+7=5/4(X+5). Line u includes the point (10,–8) and is perpendicular to line t

 What is the equation of line u? Write the equation in slope-intercept form. Write the numbers in the equation as simplified proper fractions, improper fractions, or integers.

Answer 1

Since line u is perpendicular to line t then it's slope is the opposite reciprocal of the slope of line t.

Given the Point-Slope Form y - y₁ = m(x - x₁) of Line t:

y + 7= 5/4(X + 5)

The slope of line t is m = 5/4

so the slope of line u is -4/5 (opposite reciprocal of 5/4)

Given that line u includes the point (10,–8). Use this point and the slope m = −4/5 in the​ point-slope form of a line to write the equation:

y − y₁ = m (x − x₁) This is the point-slope form of a line.

y − –8 = −4/5(x − 10) Substitute the known values.

y + 8 = −4/5x + 8 Use the distributive property.

Isolate y on the left side of the equation to write the equation in slope-intercept form:

y + 8 = −4/5x + 8

y = −4/5x Subtract 8 from both sides of the equation and simplify.

Answer 2

Here are the steps to solve this problem:

1) First isolate y on one side of the equation you are given, first by multiplying everything in the parentheses (x+5) by 5/4, so that you have y+7 = 5/4x + 25/4 (you can simplify the fractions at this step if you would like)

2) isolate y on one side of the equation, and simplify your equation. You now have the equation in y = mx + b form

3) Perpendicular lines have slopes that are negative reciprocals of each other - for example, if you have a line with a slope of 2 (you can also write 2 as 2/1), then its perpendicular line would have a slope of -1/2. With this information you can use the equation you found above to find the slope of line u.

4). Now that you have the slope of line u, write out the following equation: u = mx + b where you replace m with the slope you calculated in step 3

5) plug in x and y (u) values from the point u intersects about (10, -8) into the equation from step 4. Then solve for the missing value in the equation, which would be b.

6) Finally, put together all the information you have obtained in these steps. the equation will be u = mx + b where m is the slope you calculated in step 3, and b is the number you calculated in step 5.

I hope this helps, feel free to reach out for a session if you would like further help on this subject!