Question

Need help with two questions!!

Answer 1

the slope of A is twice the slope of B

y =-2x -4

Explanation:

function A = 6x-1

m=6

b=-1

Function B

(0,1) ( 1,4)

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

= (4-1)/(1-0)

= 3/1

= 3

slope intercept form the y intercept is 1

y=mx+b

y = 3x+1

compare the slopes

ma = 6

mb = 3

ma is 2 times mb

(-2,0)

(0,-4)

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

= (-4-0)/(0--2)

= (-4-0)/(0+2)

= -4/2

m=-2

the y intercept is -4

slope intercept form is y = mx+b

y =-2x -4

Answer 2

Couple things to note:

1. Slope-intercept form is y = mx + b, where m is the slope and b is the y-intercept.
2. Slope can be calculated using any two points on a line and the formula y₁ - y₂ / x₁ - x₂.

For the first problem, we know the slope of Function A is 6 (refer to slope-intercept form above). To compare the slopes of Function A and Function B, first find the slope of Function B.

Use y₁ - y₂ / x₁ - x₂. Two points on the line are (0, 1) and (-1, -2). Plug these into the formula accordingly and solve for slope.

y₁ - y₂ / x₁ - x₂

1 - (-2) / 0 - (-1)

1 + 2 / 0 + 1

3 / 1

3

The slope of Function B is 3. This is half of 6 (the slope of Function A), so the correct answer to question 1 is the first option: Slope of Function B = 2 × Slope of Function A.

For the second problem, substitute m and b in y = mx + b according to the graph. b is the y-intercept (the point at which the line intersects the y-axis); it is (0, -4), or -4. This gives us

y = mx - 4

We must now find m. Follow the same steps above to find slope. Our two points are (-2, 0) and (0, -4).

y₁ - y₂ / x₁ - x₂

0 - (-4) / -2 - 0

0 + 4 / -2

4 / -2

-2

Substitute.

y = -2x - 4

The first option is the correct answer.