Question

The graph of linear function `g` passes through the points (-4,4) and (4,6)`as shown. What are the slope and y-intercept of the graph `g`?

Answer 1

To find the slope of the graph `g`, we can use the formula:

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

Using the points (-4,4) and (4,6), we have:

m = (6 - 4) / (4 - (-4))
= 2 / 8
= 1/4

Therefore, the slope of the graph `g` is 1/4.

To find the y-intercept of the graph `g`, we can use the slope-intercept form of a linear equation:

y = mx + b

where m is the slope and b is the y-intercept.

Using the point (-4,4), we can substitute the values into the equation to find b:

4 = (1/4)(-4) + b

Multiplying 1/4 by -4 gives:

4 = -1 + b

Adding 1 to each side, we get:

5 = b

Therefore, the y-intercept of the graph g is 5.

Hence, the slope of the graph `g` is 1/4 and the y-intercept is 5.