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
We can first find the slope of the line using the formula:
slope = (change in y)/(change in x)
To find the change in y, we subtract the y-coordinates of the two points:
change in y = 5 - (-1) = 6
To find the change in x, we subtract the x-coordinates of the two points:
change in x = 5 - (-5) = 10
Therefore, the slope is:
slope = (change in y)/(change in x) = 6/10 = 3/5
The y-intercept is the value of y when x = 0. To find the y-intercept, we can substitute one of the points into the equation of the line. Let's use the point (5, 5):
5 = (3/5)(5) + b
Multiplying both sides of the equation by 5, we get:
25 = 15 + 5b
Subtracting 15 from both sides of the equation, we get:
10 = 5b
Dividing both sides of the equation by 5, we get:
b = 2
Therefore, the y-intercept is 2.
So the slope of the graph g is 3/5 and the y-intercept is 2.