23.
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?
The slope of a linear function can be found using the formula:
slope = (change in y) / (change in x)
By looking at the two given points (-4, 4) and (4, 6), we can calculate the slope as follows:
slope = (6 - 4) / (4 - (-4))
slope = (6 - 4) / 8
slope = 2 / 8
slope = 1/4
Therefore, the slope of the graph g is 1/4.
To find the y-intercept, we can use the equation of a straight line in slope-intercept form:
y = mx + b
Where:
m is the slope
x and y are coordinates of a point on the line
b is the y-intercept
Using the point (4, 6) and the slope 1/4, we can substitute these values into the equation:
6 = (1/4) * 4 + b
6 = 1 + b
b = 6 - 1
b = 5
Therefore, the y-intercept of the graph g is 5.
In summary, the slope of the graph g is 1/4 and the y-intercept is 5.