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

The slope-intercept form: y= mx + b

m - slope

b - y-intercept

The formula of a slope:

$m=\dfrac{y_2-y_1}{x_2-x_1}$

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

$m=\dfrac{5-2}{5-6}=\dfrac{3}{-1}=-3$

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

Answer 2

Answer:

y = -3x + 20

Step-by-step 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

=====

(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