Find the x and y Intercepts y-6=2(3x-4)

$y - 6 = 2 (3 x - 4)$

Step 1

Find the x-intercepts.

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

$(0) - 6 = 2 (3 x - 4)$

Solve the equation.

Rewrite the equation as $2 (3 x - 4) = (0) - 6$ .

$2 (3 x - 4) = (0) - 6$

Subtract $6$ from $0$ .

$2 (3 x - 4) = - 6$

Divide each term in $2 (3 x - 4) = - 6$ by $2$ and simplify.

Divide each term in $2 (3 x - 4) = - 6$ by $2$ .

$\frac{2 (3 x - 4)}{2} = \frac{- 6}{2}$

Simplify the left side.

Cancel the common factor of $2$ .

Cancel the common factor.

$\frac{2 (3 x - 4)}{2} = \frac{- 6}{2}$

Divide $3 x - 4$ by $1$ .

$3 x - 4 = \frac{- 6}{2}$

Simplify the right side.

Divide $- 6$ by $2$ .

$3 x - 4 = - 3$

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

Add $4$ to both sides of the equation.

$3 x = - 3 + 4$

Add $- 3$ and $4$ .

$3 x = 1$

Divide each term in $3 x = 1$ by $3$ and simplify.

Divide each term in $3 x = 1$ by $3$ .

$\frac{3 x}{3} = \frac{1}{3}$

Simplify the left side.

Cancel the common factor of $3$ .

Cancel the common factor.

$\frac{3 x}{3} = \frac{1}{3}$

Divide $x$ by $1$ .

$x = \frac{1}{3}$

x-intercept(s) in point form.

x-intercept(s): $(\frac{1}{3}, 0)$

Step 2

Find the y-intercepts.

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

$y - 6 = 2 (3 (0) - 4)$

Solve the equation.

Simplify $2 (3 (0) - 4)$ .

Multiply $3$ by $0$ .

$y - 6 = 2 (0 - 4)$

Subtract $4$ from $0$ .

$y - 6 = 2 \cdot - 4$

Multiply $2$ by $- 4$ .

$y - 6 = - 8$

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

Add $6$ to both sides of the equation.

$y = - 8 + 6$

Add $- 8$ and $6$ .

$y = - 2$

y-intercept(s) in point form.

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

Step 3

List the intersections.

x-intercept(s): $(\frac{1}{3}, 0)$

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

Step 4

Find the x and y Intercepts y-6=2(3x-4)

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