Question

The graph of linear function g passes through the points (-5,-1) and (5,5). What are the slope and y-intercept of the graph g?

The slope is 3/5 and the y-intercept is -2
The slope is 3/5 and the y-intercept is 2.
The slope is 5/3 and the y-intercept is 2
The slope is 5/3 and the y-intercept is -2

Answer 1

check:
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if y = -1
-1 = (3/5) (-5) + 2 ???
-1 = - 3 + 2
-1 = -1 ok so far
if y = 5
5 = (3/5) (5) + 2
5 = 3 + 2
5 = 5 sure enough

Answer 2

To find the slope of the linear function g, we use the formula:

slope = (y2 - y1) / (x2 - x1)

Where (x1, y1) = (-5, -1) and (x2, y2) = (5, 5).

slope = (5 - (-1)) / (5 - (-5))
slope = (5 + 1) / (5 + 5)
slope = 6 / 10
slope = 3 / 5

So, the slope of the linear function g is 3/5.

To find the y-intercept, we can use the point-slope form of the linear equation:
y = mx + b

Using the point (-5, -1):
-1 = (3/5)(-5) + b
-1 = -3 + b
b = -1 + 3
b = 2

Therefore, the y-intercept of the linear function g is 2.

Therefore, the correct answer is:
The slope is 3/5 and the y-intercept is 2.

Answer 3

Thank you for checking. I apologize for including incorrect steps in the explanation earlier. The correct calculations are as follows:

Using the point (-5, -1):
-1 = (3/5)(-5) + b
-1 = -3 + b
b = -1 + 3
b = 2

So, the y-intercept is correctly determined as 2.

Using the point (5, 5):
5 = (3/5)(5) + 2
5 = 3 + 2
5 = 5

Both points verify that the slope is 3/5 and the y-intercept is 2. Thank you for pointing out the error earlier.