Find the x and y Intercepts -4x+7=2y-3

$- 4 x + 7 = 2 y - 3$

Step 1

Find the x-intercepts.

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

$- 4 x + 7 = 2 (0) - 3$

Solve the equation.

Simplify $2 (0) - 3$ .

Multiply $2$ by $0$ .

$- 4 x + 7 = 0 - 3$

Subtract $3$ from $0$ .

$- 4 x + 7 = - 3$

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

Subtract $7$ from both sides of the equation.

$- 4 x = - 3 - 7$

Subtract $7$ from $- 3$ .

$- 4 x = - 10$

Divide each term in $- 4 x = - 10$ by $- 4$ and simplify.

Divide each term in $- 4 x = - 10$ by $- 4$ .

$\frac{- 4 x}{- 4} = \frac{- 10}{- 4}$

Simplify the left side.

Cancel the common factor of $- 4$ .

Cancel the common factor.

$\frac{- 4 x}{- 4} = \frac{- 10}{- 4}$

Divide $x$ by $1$ .

$x = \frac{- 10}{- 4}$

Simplify the right side.

Cancel the common factor of $- 10$ and $- 4$ .

Factor $- 2$ out of $- 10$ .

$x = \frac{- 2 (5)}{- 4}$

Cancel the common factors.

Factor $- 2$ out of $- 4$ .

$x = \frac{- 2 \cdot 5}{- 2 \cdot 2}$

Cancel the common factor.

$x = \frac{- 2 \cdot 5}{- 2 \cdot 2}$

Rewrite the expression.

$x = \frac{5}{2}$

x-intercept(s) in point form.

x-intercept(s): $(\frac{5}{2}, 0)$

Step 2

Find the y-intercepts.

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

$- 4 \cdot 0 + 7 = 2 y - 3$

Solve the equation.

Rewrite the equation as $2 y - 3 = - 4 \cdot 0 + 7$ .

$2 y - 3 = - 4 \cdot 0 + 7$

Simplify $- 4 \cdot 0 + 7$ .

Multiply $- 4$ by $0$ .

$2 y - 3 = 0 + 7$

Add $0$ and $7$ .

$2 y - 3 = 7$

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

Add $3$ to both sides of the equation.

$2 y = 7 + 3$

Add $7$ and $3$ .

$2 y = 10$

Divide each term in $2 y = 10$ by $2$ and simplify.

Divide each term in $2 y = 10$ by $2$ .

$\frac{2 y}{2} = \frac{10}{2}$

Simplify the left side.

Cancel the common factor of $2$ .

Cancel the common factor.

$\frac{2 y}{2} = \frac{10}{2}$

Divide $y$ by $1$ .

$y = \frac{10}{2}$

Simplify the right side.

Divide $10$ by $2$ .

$y = 5$

y-intercept(s) in point form.

y-intercept(s): $(0, 5)$

Step 3

List the intersections.

x-intercept(s): $(\frac{5}{2}, 0)$

y-intercept(s): $(0, 5)$

Step 4

Find the x and y Intercepts -4x+7=2y-3

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