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Answer:
Please check the complete explanation below.
Step-by-step explanation:
We know that the slope-intercept form of the line equation
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
Answer:
The number of meters Robert will beat Sam is 12 meters.
Step-by-step explanation:
Given:
When Paul crossed the finish line of a 60-meter race, he was ahead of Robert by 10 meters and ahead of Sam by 20 meters. Suppose Robert and Sam continue to race to the finish line without changing their rates of speed.
Find:
the number of meters by which Robert will beat Sam
Step 1 of 1
When Paul finishes, Robert has run 60-10=50 meters and Sam has run 60-20=40 meters.
Therefore, when Robert and Sam run for the same amount of time, Sam covers of the distance that Robert covers. So, while Robert runs the final 10 meters of the race, Sam runs
meters.
This means Robert's lead over Sam increases by 2 more meters, and he beats Sam by 10+2=12 meters.