A linear function 'f' models a relationship in which the dependent variable decreases 3 units for every 2 units the independent variable increases. The value of the function at 0 is 5. Identify the slope, y-intercept, and x-intercept.
+223 The dependent variable is the y value and the independent variable is the x value.
So since the slope is change in y over change in x then the slope equals -3/2
Using point slope form, we can create a function to find the y and x intercepts (although the y intercept is basically given in the problem)
y - y1 = m(x - x1)
m = slope
y1 = the y value the problem provides
x1 = the x value the problem provides
So the equation for the line is:
y - 5 = -3/2(x - 0)
The y intercept is found when x equals zero. Since the problem gives us a point where x equals zero we know that the y intercept is (0, 5).
To find the x intercept we need to set the y value equal to zero in the equation.
0 - 5 = -3/2(x - 0) ----> -5 = -3/2x
Now we multiply both sides by the reciprocal of -3/2 to isolate x
10/3 = x
Now we know the x intercept is (10/3, 0)
