Question

Please help! 30pts!

I don't know this... :(

Answer 1

slope formula: m = (y2 - y1) / (x2 - x1)

3. (1, -5) and (4, 1); y2 = 4, y1 = 1, x2 = 1, x1 = -5

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

m = (1 - (-5)) / (4 - 1)

m = 6 / 3

m = 2

4. (-1, 3) and (4, -7); x2 = -7, x1 = 3, y2 = 4, y1 = -1

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

m = (-7 - 3) / (4 - (-1))

m = -10 / 5

m = -2

5. Find the slope of the line whose equation is 4x - 6y = 12

The first step is to convert the equation to slope-intercept form: y = mx + b, where m = slope and b = y-intercept.

4x - 6y = 12

4x - 6y - 4x = 12 - 4x

(-6y) / (-6) = (12 - 4x) / (-6)

y = (12 / -6) - (4x / -6)

y = -2 - (- 2/3x)

y = -2 + 2/3 x

y = 2/3 x - 2

The resulting equation gives us the following information:

slope (m) = 2/3

y - intercept (b) = -2

Hope this helps you understand the process of finding slopes!

Answer 2

A, D and B

Explanation:

To calculate the slope m between 2 points use the gradient formula

m = ( y₂ - y₁ ) / ( x₂ - x₁ )

(3)

let (x₁, y₁ ) = (1, - 5) and (x₂, y₂ ) = (4, 1)

m =
`(1+5)/(4-1)` =
`(6)/(3)` = 2

(4)

let (x₁, y₁ ) = (- 1, 3) and (x₂, y₂ ) = (4, - 7)

m =
`(-7-3)/(4+1)` =
`(-10)/(5)` = - 2

(5)

the equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y-intercept )

rearrange 4x - 6y = 12 into this form

subtract 4x from both sides

- 6y = - 4x + 12 ( divide all terms by - 6 )

y =
`(2)/(3)` x - 2 ← in slope-intercept form

with slope m =
`(2)/(3)`