Question

image shows a graph with points (1,10) and (-1,4).
Write the equation of the linear function shown on the graph.

Answer 1

To find the equation of the linear function, we need to find the slope (m) and the y-intercept (b) of the line.

First, we find the slope:
m = (y2 - y1) / (x2 - x1)
m = (4 - 10) / (-1 - 1)
m = -6 / -2
m = 3

Next, we can use the point-slope form of a linear equation, y - y1 = m(x - x1), with the point (-1, 4):
y - 4 = 3(x + 1)

Now, we can simplify the equation:
y - 4 = 3x + 3
y = 3x + 7

Therefore, the equation of the linear function shown on the graph is y = 3x + 7.

Answer 2

Answer choices:
y=2x+2
y=2x−2
y=−2x+2
y=−2x−2

Answer 3

The correct answer choice is: y = 2x + 2

Explanation:
From the given points (1,10) and (-1,4), we calculate the slope using the formula:
m = (y2 - y1) / (x2 - x1)
m = (4 - 10) / (-1 - 1)
m = -6 / -2
m = 3

Now that we have the slope, we can use the point-slope form of a linear equation with the point (1,10):
y - 10 = 3(x - 1)

Simplifying the equation:
y - 10 = 3x - 3
y = 3x + 7

Therefore, the equation of the linear function shown on the graph is y = 3x + 7. This equation doesn't match any of the given answer choices.