The graph of linear function g passes through the points −5,−1and 5, 5,as shown. What are the slope and y-intercept of the graph g?
To find the slope, we use the formula:
m = (y2 - y1) / (x2 - x1)
Using the points (-5, -1) and (5, 5), we have:
m = (5 - (-1)) / (5 - (-5))
m = 6 / 10
m = 3/5
Therefore, the slope of the graph is 3/5.
To find the y-intercept, we can use the point-slope form of a linear equation:
y - y1 = m(x - x1)
Using the point (5, 5) and the slope 3/5, we have:
y - 5 = (3/5)(x - 5)
Simplifying, we get:
y - 5 = (3/5)x - 3
y = (3/5)x + 2
Therefore, the y-intercept of the graph is 2.