Question

Find the equation of a line with the given points.(put your answers in the form y=mx+b)(6,2)(5,5)

Answer 1

y = -3x + 20

Explanation:

(a) Slope

The point-slope formula for a straight line is

y₂ - y₁ = m(x₂ - x₁) Insert the points

2 - 5 = m(6 - 5)

-3 = m×1

m = -3

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(b) y-intercept

y₂ - y₁ = m(x₂ - x₁)

y₂ - 5 = -3(x₂ - 5) Remove parentheses

y₂ - 5 = -3x₂ - 15 Add 5 to each side

y = -3x + 20

Answer 2

The slope-intercept form: y= mx + b

m - slope

b - y-intercept

The formula of a slope:

`m=(y_2-y_1)/(x_2-x_1)`

We have the points (6, 2) and (5, 5). Substitute:

`m=(5-2)/(5-6)=(3)/(-1)=-3`

Therefore we have y = -3x + b.

Put the coordinates of the point (5, 5) to the equation:

5 = -3(5) + b

5 = -15 + b add 15 to both sides

20 = b

Answer: y = -3x + 20