Question

Yah another notability can anyone help please?

Answer 1

Here's what I get

Explanation:

1. Interpreting graphs

a. Identifying slope and intercept

Line A

The line passes through the points (0, 4) and (3, 0).

`\text{Slope} = (y_(2) -y_(1))/( x_(2) -x_(1)) = (0 - 4 )/(3 - 0) = -(4)/(3)`

y-intercept = (0, 4)

x-intercept = (3, 0)

Line B

The line passes through the points (-2, 0) and (0, 2).

`\text{Slope} = (2 - 0)/(0 - (-2)) = -(2)/(0 + 2)= (2)/(2) = 1`

y-intercept = (0, 2)

x-intercept = (-2, 0)

Line C

The line passes through the points (0, -4) and (2, 0)

`\text{Slope} = (0 - (-4) )/(2 - 0) = (0 + 4)/(2)= (4)/(2) = 2`

y-intercept = (0, -4)

x-intercept = (2, 0)

`\begin{array}{cccc}\textbf{Line}& \textbf{Rate}& \textbf{y-intercept} & \textbf{x-intercept}\\\textbf{A} & -(4)/(3) & (0,4) & (3, 0)\\\textbf{B} & 2 & (0, 2) & (-4, 0)\\\textbf{C} & 1 & (0, -4) & (2, 0)\\\end{array}`

b. Matching graphs to equations

The graphs all have different slopes: -⁴/₃, 1, and 2.

The graph with the negative slope is Line A.

The graph with the steepest positive slope is Line C.

The graph with a less steep slope is Line B. So,

y = 3 - x ⟶ Line A

y = 2+ x ⟶ Line B

y = -4 + 2x ⟶ Line C

2. Finding Slope, intercepts, and equations

a.

`\text{Slope} = (y_(2) -y_(1))/( x_(2) -x_(1)) = (6 - 3)/(6 - 0) = (3)/(6) =(1)/(2)`

y-intercept = (0, 3)

y = 3 + ½x

b.

`\text{Slope} = (6 - 18)/(6 - 2) = -(12)/(4) = -3`

That means, if we increase x by two units, we decrease y by six units.

If we start at (2, 18) and decrease x by two units, we increase y by six units. Then, y = 24;

y-intercept = (0, 24)

y = 24 - 3x

c.

`\text{Slope} = (9 - 9)/(8 - 2) = (0)/(6) = 0`

That means, whatever we do to x, the value of y does not change.

y-intercept = (0, 9)

y = 9 + 0x

The equation is

y = 9