Find the x and y Intercepts -6x+3y=-7

$- 6 x + 3 y = - 7$

Step 1

Find the x-intercepts.

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

$- 6 x + 3 (0) = - 7$

Solve the equation.

Simplify $- 6 x + 3 (0)$ .

Multiply $3$ by $0$ .

$- 6 x + 0 = - 7$

Add $- 6 x$ and $0$ .

$- 6 x = - 7$

Divide each term in $- 6 x = - 7$ by $- 6$ and simplify.

Divide each term in $- 6 x = - 7$ by $- 6$ .

$\frac{- 6 x}{- 6} = \frac{- 7}{- 6}$

Simplify the left side.

Cancel the common factor of $- 6$ .

Cancel the common factor.

$\frac{- 6 x}{- 6} = \frac{- 7}{- 6}$

Divide $x$ by $1$ .

$x = \frac{- 7}{- 6}$

Simplify the right side.

Dividing two negative values results in a positive value.

$x = \frac{7}{6}$

x-intercept(s) in point form.

x-intercept(s): $(\frac{7}{6}, 0)$

Step 2

Find the y-intercepts.

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

$- 6 \cdot 0 + 3 y = - 7$

Solve the equation.

Simplify $- 6 \cdot 0 + 3 y$ .

Multiply $- 6$ by $0$ .

$0 + 3 y = - 7$

Add $0$ and $3 y$ .

$3 y = - 7$

Divide each term in $3 y = - 7$ by $3$ and simplify.

Divide each term in $3 y = - 7$ by $3$ .

$\frac{3 y}{3} = \frac{- 7}{3}$

Simplify the left side.

Cancel the common factor of $3$ .

Cancel the common factor.

$\frac{3 y}{3} = \frac{- 7}{3}$

Divide $y$ by $1$ .

$y = \frac{- 7}{3}$

Simplify the right side.

Move the negative in front of the fraction.

$y = - \frac{7}{3}$

y-intercept(s) in point form.

y-intercept(s): $(0, - \frac{7}{3})$

Step 3

List the intersections.

x-intercept(s): $(\frac{7}{6}, 0)$

y-intercept(s): $(0, - \frac{7}{3})$

Step 4

Find the x and y Intercepts -6x+3y=-7

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