Question

Write an equation in standard form of the line passing through the points (12, 6) and (-4, 10).The equation is . (Type your answer in standard form.)

Answer 1

The equation, in the standard form is: x + 4y = 36

Explanation:

The standard form of the equation of a line has the following format:

Ax + By = C.

First, I will place the equation of the line in slope-intercept formula, which is:

y = ax + b. Then, I pass to the standard.

Passes through the point (12,6):

This means that when x = 12, y = 6.

So

y = ax + b

6 = 12a + b

b = 6 - 12a

Passes through the point (-4,10):

This means that when x = -4, y = 10. SO

10 = -4a + b

Since b = 6 - 12a

10 = -4a + (6 - 12a)

10 = -4a + 6 - 12a

10 - 6 = -4a - 12a

-16a = 4

16a = -4

a = -4/16

Simplifying by 4

a = -1/4

b = 6 - 12a = 6 - 12*(-1/4) = 6 + 3 = 9

So

y = ax + b

y = -(x/4) + 9

(x/4) + y = 9

Multiplying everything by 4

x + 4y = 36

The equation, in the standard form is: x + 4y = 36