3. The graph of linear function g passes through the points −4, 4and 4, 6,as shown. What are the slope and y-intercept of the graph g?
To find the slope of the linear function g, we can use the formula:
slope = change in y / change in x
Given the points (-4, 4) and (4, 6):
Change in y = 6 - 4 = 2
Change in x = 4 - (-4) = 8
Therefore, the slope of the linear function g is:
slope = 2 / 8 = 1/4
Now, to find the y-intercept, 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, 6) and the slope of 1/4:
6 = (1/4)(4) + b
6 = 1 + b
b = 5
Therefore, the y-intercept of the graph g is 5.
In conclusion, the slope of the graph g is 1/4 and the y-intercept is 5.