Respuesta :
Answer:
The line with the x- and y-intercepts below has the following equation:
[tex]f(x) = \frac{5x}{7} - 5[/tex]
Step-by-step explanation:
The equation of the line has the following format:
[tex]f(x) = ax + b[/tex]
We are given two points, we are going to substitute them into the above equation, and find the equation of the line given the conditions.
Solution
Starting from the y-intercept makes the solution easier, since the term a is multiplied by 0
y-intercept -5
This means that when [tex]x = 0, y = f(x) = -5[/tex], so:
[tex]f(x) = ax + b[/tex]
[tex]-5 = a(0) + b[/tex]
[tex]b = -5[/tex]
For now, the line has the following equation:
[tex]f(x) = ax - 5[/tex]
x-intercept 7
This means that when [tex]y = f(x) = 0,x = 7[/tex], so:
[tex]f(x) = ax - 5[/tex]
[tex]0 = 7(a) - 5[/tex]
[tex]7a = 5[/tex]
[tex]a = \frac{5}{7}[/tex]
So, the line with the x- and y-intercepts below has the following equation:
[tex]f(x) = \frac{5x}{7} - 5[/tex]
