Question

Find an equation of a line with the x- and y-intercepts below. Use exact fractions when necessary.

Answer 1

Answer:

The line with the x- and y-intercepts below has the following equation:

$f(x) = \frac{5x}{7} - 5$

Step-by-step explanation:

The equation of the line has the following format:

$f(x) = ax + b$

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 $x = 0, y = f(x) = -5$, so:

$f(x) = ax + b$

$-5 = a(0) + b$

$b = -5$

For now, the line has the following equation:

$f(x) = ax - 5$

x-intercept 7

This means that when $y = f(x) = 0,x = 7$, so:

$f(x) = ax - 5$

$0 = 7(a) - 5$

$7a = 5$

$a = \frac{5}{7}$

So, the line with the x- and y-intercepts below has the following equation:

$f(x) = \frac{5x}{7} - 5$