Write the equation of the linear function that models the relationship shown in the table.
(1 point)
Responses
y=x+34
y equals x plus 34
y=−10x+78
y equals negative 10 x plus 78
y=10x−2
y equals 10 x minus 2
y=10x+2
Table:
X Y
18 10
6 -3
To find the equation of the linear function, we need to find the slope and y-intercept. The slope of a linear function is calculated by taking the change in y divided by the change in x.
From the table, we can see that when x changes from 18 to 6, y changes from 10 to -3. Therefore, the change in y is -3 - 10 = -13, and the change in x is 6 - 18 = -12.
The slope of the function is then -13 / -12 = 13 / 12.
To find the y-intercept, we can choose any point from the table and substitute it into the equation y = mx + b, where m is the slope. Let's use the point (18, 10):
10 = (13 / 12) * 18 + b
10 = 1.5 * 18 + b
10 = 27 + b
b = 10 - 27
b = -17
Finally, we can write the equation of the linear function:
y = (13 / 12) * x - 17
What can you interpret about the equation y=−2x−8?(1 point)
Responses
The slope is −2, the y-intercept is −8, and the line is falling from left to right.
The slope is negative 2 , the y -intercept is negative 8 , and the line is falling from left to right.
The slope is 2, the y-intercept is −8, and the line is rising from left to right.
The slope is 2, the y -intercept is negative 8 , and the line is rising from left to right.
The slope is −2, the y-intercept is 8, and the line is rising from left to right.
The slope is negative 2 , the y -intercept is 8, and the line is rising from left to right.
The slope is −2, the y-intercept is 8, and the line is falling from left to right.
The slope is negative 2 , the y -intercept is 8, and the line is falling from left to right.
The interpretation of the equation y = -2x - 8 is:
The slope is -2, the y-intercept is -8, and the line is falling from left to right.
To find the equation of a linear function that models the relationship shown in the table, we need to determine the slope (m) and the y-intercept (b).
The slope of a linear function is calculated by finding the change in y divided by the change in x. By examining the table, we can see that when x changes by 12 (18 - 6), y changes by -13 (10 - (-3)).
Therefore, the slope (m) is -13/12.
To find the y-intercept (b), we can substitute the values of one of the points in the table into the equation y = mx + b and solve for b. Let's use the point (18, 10).
10 = -13/12 * 18 + b
Simplifying the equation:
10 = -13/12 * 18 + b
10 = -13/6 + b
Multiplying both sides by 6 to eliminate the fraction:
60 = -13 + 6b
Adding 13 to both sides:
73 = 6b
Dividing both sides by 6:
b = 73/6
Now that we have the slope (m = -13/12) and the y-intercept (b = 73/6), we can write the equation of the linear function:
y = -13/12x + 73/6
Therefore, the equation of the linear function that models the relationship shown in the table is y = -13/12x + 73/6.