Find the x and y Intercepts 8x-3y=6-4x

$8 x - 3 y = 6 - 4 x$

Step 1

Find the x-intercepts.

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

$8 x - 3 \cdot 0 = 6 - 4 x$

Solve the equation.

Simplify $8 x - 3 \cdot 0$ .

Multiply $- 3$ by $0$ .

$8 x + 0 = 6 - 4 x$

Add $8 x$ and $0$ .

$8 x = 6 - 4 x$

Move all terms containing $x$ to the left side of the equation.

Add $4 x$ to both sides of the equation.

$8 x + 4 x = 6$

Add $8 x$ and $4 x$ .

$12 x = 6$

Divide each term in $12 x = 6$ by $12$ and simplify.

Divide each term in $12 x = 6$ by $12$ .

$\frac{12 x}{12} = \frac{6}{12}$

Simplify the left side.

Cancel the common factor of $12$ .

Cancel the common factor.

$\frac{12 x}{12} = \frac{6}{12}$

Divide $x$ by $1$ .

$x = \frac{6}{12}$

Simplify the right side.

Cancel the common factor of $6$ and $12$ .

Factor $6$ out of $6$ .

$x = \frac{6 (1)}{12}$

Cancel the common factors.

Factor $6$ out of $12$ .

$x = \frac{6 \cdot 1}{6 \cdot 2}$

Cancel the common factor.

$x = \frac{6 \cdot 1}{6 \cdot 2}$

Rewrite the expression.

$x = \frac{1}{2}$

x-intercept(s) in point form.

x-intercept(s): $(\frac{1}{2}, 0)$

Step 2

Find the y-intercepts.

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

$8 (0) - 3 y = 6 - 4 \cdot 0$

Solve the equation.

Simplify $8 (0) - 3 y$ .

Multiply $8$ by $0$ .

$0 - 3 y = 6 - 4 \cdot 0$

Subtract $3 y$ from $0$ .

$- 3 y = 6 - 4 \cdot 0$

Simplify $6 - 4 \cdot 0$ .

Multiply $- 4$ by $0$ .

$- 3 y = 6 + 0$

Add $6$ and $0$ .

$- 3 y = 6$

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): $(\frac{1}{2}, 0)$

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

Step 4

Find the x and y Intercepts 8x-3y=6-4x

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