Question

Write a linear function for each line that relates to y to x

Answer 1

Answer:

Please check the complete explanation below.

Step-by-step explanation:

We know that the slope-intercept form of the line equation

$y = mx+b$

where m is the slope and b is the y-intercept

                                       ANALYZING TABLE 1

Part A)

Given table 1

x           0            1              2            3

y           1             3              5            7

From table 1, the y-intercept can be determined by setting  x=0 and checking the corresponding y-value.

so at x = 0, y = 1

Thus, the y-intercept is (0, 1).

From the graph, it is clear that the line W has a y-intercept (0, 1).

Therefore, table 1 represents the line W.

Part B)

Taking two points (0, 1) and (1, 3) to find the slope using the formula

m = (y₂-y₁) / (x₂-x₁)

m = 3-1 / 1-0 = 2/1 = 2

now substituting m = 2, and b = 1 in the slope-intercept form

y = mx+b

y = 2x+1

Thus, table 1 represents the line W with the equation line y = 2x+1

                                  ANALYZING TABLE 2

Part A)

Given table 2

x           0            1              2            3

y           0             3             6            9

From table 2, the y-intercept can be determined by setting  x=0 and checking the corresponding y-value.

so at x = 0, y = 0

Thus, the y-intercept (0, 0).

From the graph, it is clear that line F has a y-intercept (0, 0).

Therefore, table 2 represents the line F.

Part B)

Taking two points (0, 0) and (1, 3) to find the slope using the formula

m = (y₂-y₁) / (x₂-x₁)

m = 3-0 / 1-0 = 3/1 = 3

now substituting m = 3, and b = 0 in the slope-intercept form

y = mx+b

y = 3x+0

y = 3x

Thus, table 2 represents the line F with the equation y = 3x

                                    ANALYZING TABLE 3

Part A)

Given table 1

x           0            1              2            3

y           2             3             4            5

From table 3, the y-intercept can be determined by setting  x=0 and checking the corresponding y-value.

so at x = 0, y = 0

Thus, the y-intercept (0, 2).

From the graph, it is clear that line N has a y-intercept (0, 2).

Therefore, table 3 represents line N.

Part B)

Taking two points (0, 2) and (1, 3) to find the slope using the formula

m = (y₂-y₁) / (x₂-x₁)

m = 3-2 / 1-0 = 1/1 = 1

now substituting m = 1, and b = 2 in the slope-intercept form

y = mx+b

y = (1)x+2

y = x+2

Thus, table 2 represents the line N with the equation y = x+2