Find the x and y Intercepts 7x-5=4y-6

$7 x - 5 = 4 y - 6$

Step 1

Find the x-intercepts.

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

$7 x - 5 = 4 (0) - 6$

Solve the equation.

Simplify $4 (0) - 6$ .

Multiply $4$ by $0$ .

$7 x - 5 = 0 - 6$

Subtract $6$ from $0$ .

$7 x - 5 = - 6$

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

Add $5$ to both sides of the equation.

$7 x = - 6 + 5$

Add $- 6$ and $5$ .

$7 x = - 1$

Divide each term in $7 x = - 1$ by $7$ and simplify.

Divide each term in $7 x = - 1$ by $7$ .

$\frac{7 x}{7} = \frac{- 1}{7}$

Simplify the left side.

Cancel the common factor of $7$ .

Cancel the common factor.

$\frac{7 x}{7} = \frac{- 1}{7}$

Divide $x$ by $1$ .

$x = \frac{- 1}{7}$

Simplify the right side.

Move the negative in front of the fraction.

$x = - \frac{1}{7}$

x-intercept(s) in point form.

x-intercept(s): $(- \frac{1}{7}, 0)$

Step 2

Find the y-intercepts.

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

$7 (0) - 5 = 4 y - 6$

Solve the equation.

Rewrite the equation as $4 y - 6 = 7 (0) - 5$ .

$4 y - 6 = 7 (0) - 5$

Simplify $7 (0) - 5$ .

Multiply $7$ by $0$ .

$4 y - 6 = 0 - 5$

Subtract $5$ from $0$ .

$4 y - 6 = - 5$

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

Add $6$ to both sides of the equation.

$4 y = - 5 + 6$

Add $- 5$ and $6$ .

$4 y = 1$

Divide each term in $4 y = 1$ by $4$ and simplify.

Divide each term in $4 y = 1$ by $4$ .

$\frac{4 y}{4} = \frac{1}{4}$

Simplify the left side.

Cancel the common factor of $4$ .

Cancel the common factor.

$\frac{4 y}{4} = \frac{1}{4}$

Divide $y$ by $1$ .

$y = \frac{1}{4}$

y-intercept(s) in point form.

y-intercept(s): $(0, \frac{1}{4})$

Step 3

List the intersections.

x-intercept(s): $(- \frac{1}{7}, 0)$

y-intercept(s): $(0, \frac{1}{4})$

Step 4

Find the x and y Intercepts 7x-5=4y-6

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