Find the x and y Intercepts 4x-1=3y+5

$4 x - 1 = 3 y + 5$

Step 1

Find the x-intercepts.

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

$4 x - 1 = 3 (0) + 5$

Solve the equation.

Simplify $3 (0) + 5$ .

Multiply $3$ by $0$ .

$4 x - 1 = 0 + 5$

Add $0$ and $5$ .

$4 x - 1 = 5$

Move all terms not containing $x$ to the right side of the equation.

Add $1$ to both sides of the equation.

$4 x = 5 + 1$

Add $5$ and $1$ .

$4 x = 6$

Divide each term in $4 x = 6$ by $4$ and simplify.

Divide each term in $4 x = 6$ by $4$ .

$\frac{4 x}{4} = \frac{6}{4}$

Simplify the left side.

Cancel the common factor of $4$ .

Cancel the common factor.

$\frac{4 x}{4} = \frac{6}{4}$

Divide $x$ by $1$ .

$x = \frac{6}{4}$

Simplify the right side.

Cancel the common factor of $6$ and $4$ .

Factor $2$ out of $6$ .

$x = \frac{2 (3)}{4}$

Cancel the common factors.

Factor $2$ out of $4$ .

$x = \frac{2 \cdot 3}{2 \cdot 2}$

Cancel the common factor.

$x = \frac{2 \cdot 3}{2 \cdot 2}$

Rewrite the expression.

$x = \frac{3}{2}$

x-intercept(s) in point form.

x-intercept(s): $(\frac{3}{2}, 0)$

Step 2

Find the y-intercepts.

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

$4 (0) - 1 = 3 y + 5$

Solve the equation.

Rewrite the equation as $3 y + 5 = 4 (0) - 1$ .

$3 y + 5 = 4 (0) - 1$

Simplify $4 (0) - 1$ .

Multiply $4$ by $0$ .

$3 y + 5 = 0 - 1$

Subtract $1$ from $0$ .

$3 y + 5 = - 1$

Move all terms not containing $y$ to the right side of the equation.

Subtract $5$ from both sides of the equation.

$3 y = - 1 - 5$

Subtract $5$ from $- 1$ .

$3 y = - 6$

Divide each term in $3 y = - 6$ by $3$ and simplify.

Divide each term in $3 y = - 6$ by $3$ .

$\frac{3 y}{3} = \frac{- 6}{3}$

Simplify the left side.

Cancel the common factor of $3$ .

Cancel the common factor.

$\frac{3 y}{3} = \frac{- 6}{3}$

Divide $y$ by $1$ .

$y = \frac{- 6}{3}$

Simplify the right side.

Divide $- 6$ by $3$ .

$y = - 2$

y-intercept(s) in point form.

y-intercept(s): $(0, - 2)$

Step 3

List the intersections.

x-intercept(s): $(\frac{3}{2}, 0)$

y-intercept(s): $(0, - 2)$

Step 4

Find the x and y Intercepts 4x-1=3y+5

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