Find the x and y Intercepts f(x)=(-4x+15)/5

$f (x) = \frac{- 4 x + 15}{5}$

Step 1

Find the x-intercepts.

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

$0 = \frac{- 4 x + 15}{5}$

Solve the equation.

Set the numerator equal to zero.

$- 4 x + 15 = 0$

Solve the equation for $x$ .

Subtract $15$ from both sides of the equation.

$- 4 x = - 15$

Divide each term in $- 4 x = - 15$ by $- 4$ and simplify.

Divide each term in $- 4 x = - 15$ by $- 4$ .

$\frac{- 4 x}{- 4} = \frac{- 15}{- 4}$

Simplify the left side.

Cancel the common factor of $- 4$ .

Cancel the common factor.

$\frac{- 4 x}{- 4} = \frac{- 15}{- 4}$

Divide $x$ by $1$ .

$x = \frac{- 15}{- 4}$

Simplify the right side.

Dividing two negative values results in a positive value.

$x = \frac{15}{4}$

x-intercept(s) in point form.

x-intercept(s): $(\frac{15}{4}, 0)$

Step 2

Find the y-intercepts.

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

$y = \frac{- 4 \cdot 0 + 15}{5}$

Solve the equation.

Remove parentheses.

$y = \frac{- 4 \cdot 0 + 15}{5}$

Simplify $\frac{- 4 \cdot 0 + 15}{5}$ .

Cancel the common factor of $- 4 \cdot 0 + 15$ and $5$ .

Factor $5$ out of $- 4 \cdot 0$ .

$y = \frac{5 (- 4 \cdot 0) + 15}{5}$

Factor $5$ out of $15$ .

$y = \frac{5 (- 4 \cdot 0) + 5 \cdot 3}{5}$

Factor $5$ out of $5 (- 4 \cdot 0) + 5 (3)$ .

$y = \frac{5 (- 4 \cdot 0 + 3)}{5}$

Cancel the common factors.

Factor $5$ out of $5$ .

$y = \frac{5 (- 4 \cdot 0 + 3)}{5 (1)}$

Cancel the common factor.

$y = \frac{5 (- 4 \cdot 0 + 3)}{5 \cdot 1}$

Rewrite the expression.

$y = \frac{- 4 \cdot 0 + 3}{1}$

Divide $- 4 \cdot 0 + 3$ by $1$ .

$y = - 4 \cdot 0 + 3$

Simplify the expression.

Multiply $- 4$ by $0$ .

$y = 0 + 3$

Add $0$ and $3$ .

$y = 3$

y-intercept(s) in point form.

y-intercept(s): $(0, 3)$

Step 3

List the intersections.

x-intercept(s): $(\frac{15}{4}, 0)$

y-intercept(s): $(0, 3)$

Step 4

Find the x and y Intercepts f(x)=(-4x+15)/5

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