Question

A line passes through the given points. Write an equation for the line in point-slope form. Then rewrite the equation in slope-intercept form. (1 , 12) , (3, 2)

Answer 1

Explanation:

The formula for the equation of a line in point slope form is expressed as

y - y1 = m(x - x1)

Where

m represents the slope. The formula for determining slope is

Slope = (y2 - y1) /(x2 -;x1)

Where

y2 represents final value of y = 2

y1 represents initial value of y = 12

x2 represents final value of x = 3

x1 represents initial value of x = 1

Therefore,

Slope = (2 - 12)/(3 - 1) = - 10/2 = -5

Therefore, the point slope form would be

y - 12 = - 5(x - 1)

The equation for the slope-intercept form is expressed as

y = mx + c

Where c = intercept

To determine c, we would substitute m = - 5, x = 1 and y = 12 into y = mx + c. It becomes

12 = - 5 × 1 + c = - 5 + c

c = 12 + 5 = 17

The equation becomes

y = - 5x + 17

Answer 2

The answer to your question is a) y - 2 = -5(x - 3)

b) y = -5x + 17

Explanation:

Data

A (1, 12)

B (3, 2)

Process

1.- Find the slope

Formula

`m = (y2 - y1)/(x2 - x1)`

Substitution

`m = (2 - 12)/(3 - 1) = (-10)/(2) = - 5`

2.- Find the equation in point slope form

Equation

y - y1 = m(x - x1)

Substitution and equation

y - 2 = -5(x - 3)

3.- Find the slope-intercept form

Expand the point slope form

y - 2 = -5x + 15

Simplify

y = -5x + 15 + 2

Equation

y = -5x + 17