A line goes through the points (5, -1) and (7, -5). What is a possible equation to a new line that is perpendicular?

Ok, so you are given an equation in standard form, 5x+4y=2, and a point, (7, 5). You are being asked to write the equation for a line that is parallel to the equation in standard from, and that includes the point (7, 5).  

First, let's start by finding the slope of your new line. We know that it needs to have the same slope as 5x+4y=2, because parallel lines have the same slopes. To do that, we need to put the equation into slope-intercept form (y=mx+b), which means we need to isolate the "y."  

 5x+4y=2

-5x     -5x  (subtract 5x from both sides to move it to the right side of your equation)

4y = 2 - 5x

/4  /4  /4 (divide all the terms by 4 to get "y" by itself)

y = (1/2) - (5/4)x  ... I suggest leaving your slope as a fraction.

Now, we know that our slope, m , is going to be -(5/4).  

Next, we are going to use our slope, -(5/4), and point, (7, 5), to find the b-value (y-intercept) of your new line. Let's plug in what we know:

y = 5

m = -(5/4)

x = 7

y=mx+b

5=(-5/4)(7) + b  -> I plugged in what we knew for y, m, and x.  

5 = -(35/4) + b  -> I multiplied the numbers in the numerator (5 x 7) to get 35/4

20/4 = -(35/4) + b -> I converted 5 into a faction with a denominator of 4 by multiplying by (4/4)

+(35/4) +(35/4)  -> I add (35/4) to both sides to isolate b

55/4 = b ... or b = 13.74

Answer:  

m = -(5/4)

b = 13.75

The equation perpendicular to the line going through the points (5, -1) and (7, -5) is [tex]y=\frac{1}{2} x-\frac{7}{2}[/tex]

The line passes through the points (5, -1) and (7, -5)

That is [tex]x_1=5, y_1=-1, x_2=7, y_2=-5[/tex]

Calculate the slope(m) using the formula below:

[tex]m=\frac{y_2-y_1}{x_2-x_1} \\\\m=\frac{-5-(-1)}{7-5} \\\\m=\frac{-4}{2}\\\\m=-2[/tex]

The equation of the new line perpendicular to the line above will be given as:

[tex]y-y_1=\frac{-1}{m} (x-x_1)\\\\y-(-1)=\frac{-1}{-2} (x-5)\\\\y+1=\frac{1}{2}(x-5)\\\\y=\frac{1}{2} x-\frac{5}{2} -1\\\\y=\frac{1}{2} x-\frac{7}{2}[/tex]

The equation perpendicular to the line going through the points (5, -1) and (7, -5) is [tex]y=\frac{1}{2} x-\frac{7}{2}[/tex]

Learn more here: https://brainly.com/question/17684243

how do I solve this linear inequality?
5x - 7 > 4x + 8

To determine the number of trout in a lake, a conservationist catches 149 trout,
tags them and throws them back into the lake. Later, 36 trout are caught; 12 of
them are tagged. How many trout would the conservationist expect to be in the
lake?

I need help asap!!!!
What is the slope of the line on the graph below?
2 IV
-2 -1
1
2
3
4
5
6.
7
8
х
-2
4
45
-6
-7
48
1

another mathh question

Kelly has 15 blue bracelets and 12 green bracelets. What is the ratio of Kelly’s blue bracelets to green bracelets?

Find the length of the diagonal in rectangle using image 3353

helppppppp pleaseeeee


if somebody can answer this I'll really really appreciate it

find the slope of the line through these pair of points. (17, –6), (–11, 7)​

Find the equation of a line parallel to y = -5x – 10 that passes through the point
(-5,0).

seven million five hundred and forty-two eight hundred in number form pls

Find the set of values for which 5/x > 15

what is the improper fraction 2 7/8what is the improper fraction 8 2/3

I need help please

Which value is the closest to
0.9 • 997

a. 1,000
b. 81
c. 10,000
d. 10

Answer with supporting work:

a square has a shaded part with 7cm and 4cm and 40 cm. workout the percentage of the are inside the square that is shaded

HELPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPP

this is due in less the 30 minutes and this is my last question on the assignment please help and show work. will give brainliest

Jane needs to make a four-letter password. If the first letter has to be a vowel, how many possibilities are there to choose from where y is not a vowel

Megan spent half of her paycheck on an iPad. Over the weekend she earned $12 from babysitting. If she has $514.50 now. Write and equation and solve to find out how much was her paycheck

4,00
.
5. Mr. Brown has $410,000 in a retirement account that earns 3.85% interest each year. Find the
amount earned each year by his investment.

!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!4

The chances that you will be ticketed for illegal parking on campus are about 1/3. During the last nine days, you have illegally parked every day and have NOT been ticketed (you lucky person!). Today, on the 10th day, you again decide to park illegally. The chances that you will be caught are:

Can you please answer this world problem? And please don't mind the numbers on top.

How do I answer this question?

Find an
angle in each quadrant with a common reference angle with 280°, from
0°

A line includes the points (7, –7) and (11, –3). What is its equation in slope-intercept form?

Still won his election by a margin of 7 to 2 his opponent had 3492 votes how many votes did Steve have
Help ASAP

What is the probability that out of 125 babies born, at least 50 will be girls?
Assume that boys and girls are equally probable, and round your answer to the nearest tenth of a percent.
A. 70.4%
B. 99.0%
C. 10.5%
D. 51.2%

Sam and Andre shared a number of pennies in the ratio 8:3. They received a total of 671 pennies. How many more pennies did Sam receive than Andre?

PLEASE HELP!!!!!!!!!!!!!!!!!!!!

6) Jennilsa is making ice cream. The recipe requires ½ cup of milk and 1 ½ teaspoons of sugar. Jennilsa wants to make the recipe using 1 cup of milk. To maintain the ratio, how much sugar is required when 1 cup of milk is used?