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

$- 4 x + 7 y = 3$

Step 1

Find the x-intercepts.

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

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

Solve the equation.

Simplify $- 4 x + 7 (0)$ .

Multiply $7$ by $0$ .

$- 4 x + 0 = 3$

Add $- 4 x$ and $0$ .

$- 4 x = 3$

Divide each term in $- 4 x = 3$ by $- 4$ and simplify.

Divide each term in $- 4 x = 3$ by $- 4$ .

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

Simplify the left side.

Cancel the common factor of $- 4$ .

Cancel the common factor.

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

Divide $x$ by $1$ .

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

Simplify the right side.

Move the negative in front of the fraction.

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

x-intercept(s) in point form.

x-intercept(s): $(- \frac{3}{4}, 0)$

Step 2

Find the y-intercepts.

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

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

Solve the equation.

Simplify $- 4 \cdot 0 + 7 y$ .

Multiply $- 4$ by $0$ .

$0 + 7 y = 3$

Add $0$ and $7 y$ .

$7 y = 3$

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

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

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

Simplify the left side.

Cancel the common factor of $7$ .

Cancel the common factor.

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

Divide $y$ by $1$ .

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

y-intercept(s) in point form.

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

Step 3

List the intersections.

x-intercept(s): $(- \frac{3}{4}, 0)$

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

Step 4

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

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