Question

[x] [y]

Answer 1

Answer:

x = 1, y =   46\3

y-intercept = 2

slope(m) =  

7 - 2 \3 - 0 =  5 \3

thus,

y =  5 \3 x + 2

then, plug in values

Answer 2

Answer:

B) x = 1, y = 46/3

Step-by-step explanation:

The general equation for a straight line is

y = mx + b

Step 1. Find the slope of the line

The slope m is

m =(y₂ -y₁)/(x₂/x₁)

Two of your points are (0, 2) and (3, 7).

m = (7 – 2)/(3 – 0)

m  = 5/3

Step 2. Find the equation of the line

Use point (0, 2).

2 = ⁵/₃ × 0 + b

2 = 0 + b

b = 2

The equation of the line is

y = ⁵/₃x + 2

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Step 3.Find the coordinates of the first missing point.

(x, 11/3)

11/3 = ⁵/₃x + 2     Multiply each side by 3

  11 = 5x + 6       Subtract 6 from each side

  5 = 5x              Divide each side by 5

  x = 1

The missing value is x = 1.

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Step 4. Find the coordinates of the second missing point

(8, y)

  y = ⁵/₃ × 8 + 2   Multiply each side by 3

3y  = 40 + 6        Combine like terms

3y = 46               Divide each side by 3

y = 46/3

The missing value is y = 46/3.

Your three known points give the green line in the graph below.

The orange dot represents the first missing point at (1, 11/3).

The red dot represents the second missing point at (8, 46/3).