Question

Write an equation in standard form for a line that goes through the points(5,1) and (7,-3).

Answer 1

Answer:

Equation of line =

y = -2x + 11

Step-by-step explanation:

Using the formula for equation of a line with two points

(y_2 - y_1) / (x_2 - x_1) = (y - y_1) / (x - x_1)

Using the points we are provided with

( 5,1)(7,-3)

x_1 = 5

y_1 = 1

x_2 = 7

y_2 = -3

Inserting those values

( -3 - 1) / (7 - 5) = (y - 1) / (x - 5)

-4/2 = (y - 1) / (x - 5)

Cross multiply

-4(x - 5) = 2 ( y - 1)

Open the brackets

-4x + 20 = 2y - 2

-4x +20 +2 = 2y

-4x + 22 = 2y

Divide through by 2 to get the value of y following the rules

y = mx + C

-4x + 22 = 2y

-4x + 22 / 2 = 2y/2

-4x + 22 / 2 = y

We can still separate

-4x / 2 + 22/ 2 = y

-2x + 11 = y

y = -2x + 11