Question

7. Which equation best represents the relationship

Answer 1

Answer:

B. y=1/4x+2

Step-by-step explanation:

Equation of a Line

We are given a graph and we must select which of the proposed equations corresponds with the graph.

Let's identify two clear points in the graph. They are (0,2) and (4,3)

Substituting x=0 in the correct equation should give y=2. All the equations but C. give y=2 when x=0

Now when x=4, y should be 3.

Substituting in the each equation:

y=4x+2 = 4*4+2=18

y=1/4(4)+2=3

y=3x+2=3*4+2=14

The only equation that passes through both points is:

B. y=1/4x+2

Answer 2

Answer:

The equation best represents the relationship  between x and y in the graph is:

y =1/4x + 2

Hence, option B is correct.

Step-by-step explanation:

The slope-intercept form of the line equation

$y = mx+b$

where

• m is the slope

• b is the y-intercept

Taking two points from the given graph

• (0, 2)

• (4, 3)

Determining the slope between (0, 2) and (4, 3)

• (x₁, y₁) = (0, 2)

• (x₂, y₂) = (4, 3)

Using the formula

Slope = m =  [y₂ - y₁] /  [x₂ - x₁]

               =  [3 - 2] / [4 - 0]

               = 1 / 4            

Thus, the slope of the line = m = 1/4

We know that the value of the y-intercept can be determined by setting x = 0, and determining the corresponding value of y.

From the graph, it is clear

at x = 0, y = 2

Thus, the y-intercept b = 2

now substituting m = 1/4 and b = 2

y = mx+b

y =1/4x + 2

Therefore, the equation best represents the relationship  between x and y in the graph is:

y =1/4x + 2

Hence, option B is correct.