Find the x and y Intercepts (5x-18)/(x-7)

$\frac{5 x - 18}{x - 7}$

Step 1

Write $\frac{5 x - 18}{x - 7}$ as an equation.

$y = \frac{5 x - 18}{x - 7}$

Step 2

Find the x-intercepts.

To find the x-intercept(s), substitute in $0$ for $y$ and solve for $x$ .

$0 = \frac{5 x - 18}{x - 7}$

Solve the equation.

Set the numerator equal to zero.

$5 x - 18 = 0$

Solve the equation for $x$ .

Add $18$ to both sides of the equation.

$5 x = 18$

Divide each term in $5 x = 18$ by $5$ and simplify.

Divide each term in $5 x = 18$ by $5$ .

$\frac{5 x}{5} = \frac{18}{5}$

Simplify the left side.

Cancel the common factor of $5$ .

Cancel the common factor.

$\frac{5 x}{5} = \frac{18}{5}$

Divide $x$ by $1$ .

$x = \frac{18}{5}$

x-intercept(s) in point form.

x-intercept(s): $(\frac{18}{5}, 0)$

Step 3

Find the y-intercepts.

To find the y-intercept(s), substitute in $0$ for $x$ and solve for $y$ .

$y = \frac{5 (0) - 18}{(0) - 7}$

Solve the equation.

Remove parentheses.

$y = \frac{5 (0) - 18}{0 - 7}$

Remove parentheses.

$y = \frac{5 (0) - 18}{(0) - 7}$

Simplify $\frac{5 (0) - 18}{(0) - 7}$ .

Simplify the numerator.

Multiply $5$ by $0$ .

$y = \frac{0 - 18}{0 - 7}$

Subtract $18$ from $0$ .

$y = \frac{- 18}{0 - 7}$

Reduce the expression by cancelling the common factors.

Subtract $7$ from $0$ .

$y = \frac{- 18}{- 7}$

Dividing two negative values results in a positive value.

$y = \frac{18}{7}$

y-intercept(s) in point form.

y-intercept(s): $(0, \frac{18}{7})$

Step 4

List the intersections.

x-intercept(s): $(\frac{18}{5}, 0)$

y-intercept(s): $(0, \frac{18}{7})$

Step 5

Find the x and y Intercepts (5x-18)/(x-7)

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