Math help.?

Question

Writhe the slope-intercept form of the equation of the line through the given points.\ 

Question (1) through (-1,3) and (2,-2) 
(2) through (-5,-3) and (-1,-5)

Answer 1

1) Let the points

The formula of the slope between two points

The slope and the coordinates of either point (-1, 3) to write the equation in point-slope form.

Comments

The slope - intercept form of line equation : y = mx + b, where m = slope and b = y - intercept.

First find the slope.

Let the points are (x₁, y₁) = (- 1, 3) and (x₂, y₂) = (2, - 2).

Slope m = (y₂ -y₁)/(x₂ - x₁).

m = [- 2 - 3] / [2 - (- 1)] = - 5/3.

Next find the y - intercept.

To find y - intercept, substitute the m = - 5/3 and either point say (- 1, 3) in the slope intercept form : y = mx + b.

3 = (- 5/3)(- 1) + b

3 = 5/3 + b

b = 3 -  5/3 = (9 - 5)/3 = 4/3.

The slope intercept form of line equation is y = (- 5/3)x + 4/3.

Answer 2

2) Let the points

The formula of slope between two points

The slope and the coordinates of either point (-5, -3) to write the equation in point-slope form.

Comments

The slope - intercept form of line equation : y = mx + b, where m = slope and b = y - intercept.

First find the slope.

Let the points are (x₁, y₁) = (- 5, - 3) and (x₂, y₂) = (- 1, - 5).

Slope m = (y₂ -y₁)/(x₂ - x₁).

m = [- 5 - (- 3)] / [- 1 - (- 5)] = - 2/4 = - 1/2.

Next find the y - intercept.

To find y - intercept, substitute the m = - 1/2 and either point say (- 5, - 3) in the slope intercept form : y = mx + b.

- 3 = (- 1/2)(- 5) + b

- 3 = 5/2 + b

b = - 3 -  5/2 = (- 6 - 5)/2 = - 11/2.

The slope intercept form of line equation is y = (- 1/2)x - 11/2.