Final answer:
To find the equation of the line that goes through the given points, we need to find the slope and the y-intercept of the line. The slope of the line is 3, and it does not matter which points are used to find the slope as long as they are different. The equation of the line is y = 3x + 10.
Step-by-step explanation:
To find the equation of the line that goes through the given points, we need to find the slope and the y-intercept of the line.
a. What is the slope of the line?
To find the slope, we can choose any two points from the table and use the formula:
Slope (m) = (change in y) / (change in x)
Let's choose the points (29, 97) and (-8, -14) from the table:
(Change in y) = 97 - (-14) = 111
(Change in x) = 29 - (-8) = 37
Slope (m) = 111 / 37 = 3
Therefore, the slope of the line is 3.
b. Does it matter which points you used to find the slope of your line? Find the slope with two other points to verify your answer.
No, it does not matter which points you use to find the slope as long as the points are different.
Let's choose the points (18, 64) and (14, 52) from the table:
(Change in y) = 64 - 52 = 12
(Change in x) = 18 - 14 = 4
Slope (m) = 12 / 4 = 3
As you can see, the slope is the same as the slope we found earlier using different points, which verifies our answer.
c. How can you use a point to find the equation? Find the equation of the line.
To find the equation of the line, we can use the point-slope form of the equation:
y - y1 = m(x - x1)
Let's choose the point (29, 97) from the table and use the slope we found earlier (m = 3):
y - 97 = 3(x - 29)
y - 97 = 3x - 87
y = 3x - 87 + 97
y = 3x + 10
Therefore, the equation of the line is y = 3x + 10.
d. Once you have the slope, does it matter which point you use to find your equation? Why or why not?
No, it does not matter which point you use to find the equation because the slope is constant for the line.
How can you verify that your equation is correct?
We can verify the equation by substituting the x-values of the given points into the equation and checking if the corresponding y-values are obtained.