6 Write an equation in point-slope form given the points (-1,-7) and (2, 5). a. y - 5 = 4 (x - 2) b. y + 5 = 4 (x + 2) c. y - 2 = 4 (x - 5) d. y + 2 = 4 (x + 5)

A - y - 5= 4(x - 2)

Step-by-step explanation:

First find slope with the two points given

( -1 , -7) and ( 2 , 5)

Using

m = y_2 - y_1 / x_2 - x_1

m - slope

x_1 = -1

y_1 = -7

x_2 = 2

ÿ_2 = 5

Inserting the values

m = 5 - (-7) / 2 - (-1)

= 5 + 7 / 2 + 1

= 12 / 3

= 4

Slope is 4

Then let's proceed

y - y_1 = m ( x - x_1)

using ( 2 , 5) as x_1 and y_1 respectively

x_1 = 2

y_1 = 5

m = 4

y - 5 = m ( x - 2)

m = 4

y - 5 = 4 ( x - 2)

We are asked to give the answer in point slope form

starting with:    

5 + x - 12 = 2x - 7   

5 + x - 12 - x = 2x - 7 - x (subtract x from both sides)   

5 - 12 = x - 7 (combine and cancel x's from both sides)   

5 - 12 + 7 = x - 7 + 7 (add 7 to both sides)   

0 = x (add numbers together on both sides)       

so in order for the equation to be true, x must be 0.   

trying x = -0.5   

5 + x - 12 = 2x - 7 (original equation)   

5 + -0.5 - 12 = 2(-0.5) - 7 (plug in value of x)   

5 + -0.5 - 12 = -1 - 7 (did multiplication)   

-7.5 = -8 (did addition on both sides)       

since -7.5 is obviously not equal to -8, the value of -0.5 for x is wrong.   

trying x = 0   

5 + x - 12 = 2x - 7 (original equation)   

5 + 0 - 12 = 2(0) - 7 (plug in value of x)   

5 + 0 - 12 = 0 - 7 (did multiplication)   

-7 = -7 (did addition on both sides)       

since -7 equals -7, that demonstrates that the value of 0 for x is correct.   

trying x = 1   

5 + x - 12 = 2x - 7 (original equation)   

5 + 1 - 12 = 2(1) - 7 (plug in value of x)   

5 + 1 - 12 = 2 - 7 (did multiplication)   

-6 = -5 (did addition on both sides)       

since -6 is obviously not equal to -5, the value of 1 for x is wrong.