Question

Which graph has a slope of Two-thirds? a On a coordinate plane, a line goes through points (0, negative 1) and (2, 2). b On a coordinate plane, a line goes through points (negative 3, 1) and (0, negative 1). c On a coordinate plane, a line goes through points (0, negative 1) and (3, 1). d On a coordinate plane, a line goes through points (negative 2, 2) and (0, negative 1).

Answer 1

C. On a coordinate plane, a line goes through points (0, negative 1) and (3, 1).

Step-by-step explanation:

The way we find slope is though using y2-y1/x2-x1 as our equation. We can choose one pair of coordinates, and put the "y" on top, and the "x" on the bottom, a subtraction sign, and then the other pair of (x,y) coordinates in the same way, and solve!

We can apply this to each problem, and whichever gave us the result we're looking for, is the correct answer!

A. On a coordinate plane, a line goes through points (0, negative 1) and (2, 2).

So, we would have 2 - (-1)/2-0

Solve:

2 - (-1)/2-0

2 + 1/2-0

3/2

B. On a coordinate plane, a line goes through points (negative 3, 1) and (0, negative 1).

So, we would have 1 - (-1)/-3-0

Solve:

1 - (-1)/-3-0

1 + 1/-3-0

2/-3

C. On a coordinate plane, a line goes through points (0, negative 1) and (3, 1).

So, we would have 1 - (-1)/3-0

Solve:

1 - (-1)/3-0

1 + 1/3-0

2/3

D. On a coordinate plane, a line goes through points (negative 2, 2) and (0, negative 1).

So, we would have 2 - (-1)/-2-0

Solve:

2 - (-1)/-2-0

2 + 1/-2-0

3/-2

The only pair that gave us the answer we're looking for is C. THerefore, our answer is C.

Hope this helps!

Answer 2

The graph which has a Two-thirds slope is a line which passes through the points, (0, -1) and (3, 1)

Step-by-step explanation:

What is slope?

Slope is a ratio of change in y-coordinate w.r.t. change in x-coordinate. The net change in y coordinate is written as, Δy and the net change in x coordinate is written as, Δx.

So formula for the slope is,

m = change in y coordinate/change in x coordinate = Δy/Δx = y₂-y₁/x₂-x₁

Given that,

1. the points, (0,-1) and (2, 2)

2. the points, (-3, 1) and (0, -1)

3. the points, (0,-1) and (3, 1)

4. the points, (-2, 2) and (0, -1)

line which has slope = ?

So, we can calculate slope by using formula when two points are given,

m = y₂-y₁/x₂-x₁

x₁ = 0

y₁ = -1

x₂ = 2

y₂ = 2

m = 2-(-1)/2-0

m = 3/2

Similarly, we can calculate slopes for all the points

And, line made by the points (0,-1) and (3, 1) will give slope 2/3

Hence, the slope 2/3 has a line containing points (0,-1) and (3, 1)