Write an equation in point-slope form of the line that passes through the point (3,-5) and has a slope of 2.

ExtremeBDS [4]

-3x - y = -17
4x + 2y = 20

multiply one part of the equation so that we can be able to use the process of elimination.

(-3x - y = -17)2
4x + 2y = 20

Now we have:

-6x -2y = - 34
4x+2y= 20
------------------------
-2x = -14

Divide -2 on both sides.

-2x = -14
/-2       /-2

x = -7.

=============================================

To solve for y, we just have to substitute the value of x to any of the equation given above, that we feel comfortable with. And I'm going to choose this equation: 4x + 2y = 20

4x + 2y = 20

4(-7) + 2y = 20

-28 + 2y = 20

Add 28 on both sides

-28 + 2y = 20
+28          +28
---------------------
2y = 48
/2      /2

y = 24.

The last thing you would do is to check if the answers is correct.
All you have to do is plug in the values of x and y into both equations and see if they equal to one another.

You may have to do this by yourself :P

Anyways, if you have any questions about this topic, feel free to PM me or any other users interested. Thank you for being part of Brainly! Have a nice day!

4 0

3 years ago

What is the justification for the step taken from line 2 to line 3?

stiv31 [10]

Step-by-step explanation:

$3x+9-7x=x+10+x\\-4x+9=2x+10\\-6x+9=10\\$

In the line 2, only variables were operated with a reduction of similar terms in each side of the equation, giving as result -4x at one side, and 2x at the other side.
In the line 3, terms with variables were joined together in one side of the equation, and then, they were operate it, given as result -6X.

3 0

3 years ago

Read 2 more answers

write an equation for the perpendicular bisector of the line joining the two points. PLEASE do 4,5 and 6

myrzilka [38]

Answer:

4. The equation of the perpendicular bisector is y = $\frac{3}{4}$ x - $\frac{1}{8}$

5. The equation of the perpendicular bisector is y = - 2x + 16

6. The equation of the perpendicular bisector is y = $-\frac{3}{2}$ x + $\frac{7}{2}$

Step-by-step explanation:

Lets revise some important rules

The product of the slopes of the perpendicular lines is -1, that means if the slope of one of them is m, then the slope of the other is $-\frac{1}{m}$ (reciprocal m and change its sign)
The perpendicular bisector of a line means another line perpendicular to it and intersect it in its mid-point
The formula of the slope of a line is $m=\frac{y_{2}-y_{1}}{x_{2}-x_{1}}$
The mid point of a segment whose end points are $(x_{1},y_{1})$ and $(x_{2},y_{2})$ is $(\frac{x_{1}+x_{2}}{2},\frac{y_{1}+y_{2}}{2})$
The slope-intercept form of the linear equation is y = m x + b, where m is the slope and b is the y-intercept

4.

∵ The line passes through (7 , 2) and (4 , 6)

- Use the formula of the slope to find its slope

∵ $x_{1}$ = 7 and $x_{2}$ = 4

∵ $y_{1}$ = 2 and $y_{2}$ = 6

∴ $m=\frac{6-2}{4-7}=\frac{4}{-3}$

- Reciprocal it and change its sign to find the slope of the ⊥ line

∴ The slope of the perpendicular line = $\frac{3}{4}$

- Use the rule of the mid-point to find the mid-point of the line

∴ The mid-point = $(\frac{7+4}{2},\frac{2+6}{2})$

∴ The mid-point = $(\frac{11}{2},\frac{8}{2})=(\frac{11}{2},4)$

- Substitute the value of the slope in the form of the equation

∵ y = $\frac{3}{4}$ x + b

- To find b substitute x and y in the equation by the coordinates

of the mid-point

∵ 4 = $\frac{3}{4}$ × $\frac{11}{2}$ + b

∴ 4 = $\frac{33}{8}$ + b

- Subtract $\frac{33}{8}$ from both sides

∴ $-\frac{1}{8}$ = b

∴ y = $\frac{3}{4}$ x - $\frac{1}{8}$

∴ The equation of the perpendicular bisector is y = $\frac{3}{4}$ x - $\frac{1}{8}$

5.

∵ The line passes through (8 , 5) and (4 , 3)

- Use the formula of the slope to find its slope

∵ $x_{1}$ = 8 and $x_{2}$ = 4

∵ $y_{1}$ = 5 and $y_{2}$ = 3

∴ $m=\frac{3-5}{4-8}=\frac{-2}{-4}=\frac{1}{2}$

- Reciprocal it and change its sign to find the slope of the ⊥ line

∴ The slope of the perpendicular line = -2

- Use the rule of the mid-point to find the mid-point of the line

∴ The mid-point = $(\frac{8+4}{2},\frac{5+3}{2})$

∴ The mid-point = $(\frac{12}{2},\frac{8}{2})$

∴ The mid-point = (6 , 4)

- Substitute the value of the slope in the form of the equation

∵ y = - 2x + b

- To find b substitute x and y in the equation by the coordinates

of the mid-point

∵ 4 = -2 × 6 + b

∴ 4 = -12 + b

- Add 12 to both sides

∴ 16 = b

∴ y = - 2x + 16

∴ The equation of the perpendicular bisector is y = - 2x + 16

6.

∵ The line passes through (6 , 1) and (0 , -3)

- Use the formula of the slope to find its slope

∵ $x_{1}$ = 6 and $x_{2}$ = 0

∵ $y_{1}$ = 1 and $y_{2}$ = -3

∴ $m=\frac{-3-1}{0-6}=\frac{-4}{-6}=\frac{2}{3}$

- Reciprocal it and change its sign to find the slope of the ⊥ line

∴ The slope of the perpendicular line = $-\frac{3}{2}$

- Use the rule of the mid-point to find the mid-point of the line

∴ The mid-point = $(\frac{6+0}{2},\frac{1+-3}{2})$

∴ The mid-point = $(\frac{6}{2},\frac{-2}{2})$

∴ The mid-point = (3 , -1)

- Substitute the value of the slope in the form of the equation

∵ y = $-\frac{3}{2}$ x + b

- To find b substitute x and y in the equation by the coordinates

of the mid-point

∵ -1 = $-\frac{3}{2}$ × 3 + b

∴ -1 = $-\frac{9}{2}$ + b

- Add $\frac{9}{2}$ to both sides

∴ $\frac{7}{2}$ = b

∴ y = $-\frac{3}{2}$ x + $\frac{7}{2}$

∴ The equation of the perpendicular bisector is y = $-\frac{3}{2}$ x + $\frac{7}{2}$

8 0

3 years ago

In the United States, among a representative group of 6,006 white men and 1,126 black men, ages 70-79 at diagnosis with stage IV

Ivenika [448]

Answer:

White men diagnosed with stage IV prostatic adenocarcinoma within the age bracket of 70-79 are 1.27 times more likely to survive five years after the diagnosis of stage IV prostatic adenocarcinoma than black men.

Step-by-step explanation:

The exposure is race and the outcome is survival.

Race Alive Dead T

W 2337 3669 6006

B 344 782 1126

Relative Risk - 1.27

White men diagnosed with stage IV prostatic adenocarcinoma within the age bracket of 70-79 are 1.27 times more likely to survive five years after the diagnosis of stage IV prostatic adenocarcinoma than black men.

7 0

3 years ago

The cost T, in hundreds of dollars, of tuition and fees at many community colleges can be approximated by Upper T equals one h

Rainbow [258]

Course set of 8 and 2/3rds

7 0

3 years ago