Answer:
X-intercept: (6, 0)
Y-intercept: (0, -30)
Step-by-step explanation:
Definitions
- The y-intercept is the point on the graph where it crosses the y-axis, with coordinates of (0, b ). Thus, the corresponding x-coordinate of a y-intercept is 0.
- The x-intercept is the point on the graph where it crosses the x-axis, with coordinates of (a, 0). Hence, with the x-intercept is the value of x when y = 0.
Solutions:
Given the function, f(x) = 5(x - 4) - 10:
We could easily find the y-intercept by setting the value of x = 0.
f(0) = 5(0 - 4) - 10
f(0) = 5(- 4) - 10
f(0) = -20 - 10
f(0) = -30
Therefore, the y-intercept of the given function is (0, -30).
Similarly, we can solve for the x-intercept by setting the value of y = 0:
f(x) = 5(x - 4) - 10
0 = 5(x - 4) - 10
Distribute 5 into the parenthesis on the right-hand side of the equation:
0 = 5x - 20 - 10
Combine like terms:
0 = 5x - 30
Add 30 to both sides:
0 + 30 = 5x - 30 + 30
30 = 5x
Divide both sides by 5 to solve for the value of x:
[tex]\mathsf{\frac{30}{5}\:=\:\frac{5x}{5}}[/tex]
x = 6
Therefore, the x-intercept of the function is (6, 0).
Quick Side Note:
The given function can be transformed into its slope-intercept form, f(x) = mx + b by distributing 5 into the parenthesis:
f(x) = 5(x - 4) - 10
f(x) = 5x - 20 - 10
f(x) = 5x - 30 ⇒ This is the slope-intercept form, where the slope, m = 5, and the y-intercept, b = -30.
