Find the x and y Intercepts 2x-7y=42

$2 x - 7 y = 42$

Step 1

Find the x-intercepts.

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

$2 x - 7 \cdot 0 = 42$

Solve the equation.

Simplify $2 x - 7 \cdot 0$ .

Multiply $- 7$ by $0$ .

$2 x + 0 = 42$

Add $2 x$ and $0$ .

$2 x = 42$

Divide each term in $2 x = 42$ by $2$ and simplify.

Divide each term in $2 x = 42$ by $2$ .

$\frac{2 x}{2} = \frac{42}{2}$

Simplify the left side.

Cancel the common factor of $2$ .

Cancel the common factor.

$\frac{2 x}{2} = \frac{42}{2}$

Divide $x$ by $1$ .

$x = \frac{42}{2}$

Simplify the right side.

Divide $42$ by $2$ .

$x = 21$

x-intercept(s) in point form.

x-intercept(s): $(21, 0)$

Step 2

Find the y-intercepts.

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

$2 (0) - 7 y = 42$

Solve the equation.

Simplify $2 (0) - 7 y$ .

Multiply $2$ by $0$ .

$0 - 7 y = 42$

Subtract $7 y$ from $0$ .

$- 7 y = 42$

Divide each term in $- 7 y = 42$ by $- 7$ and simplify.

Divide each term in $- 7 y = 42$ by $- 7$ .

$\frac{- 7 y}{- 7} = \frac{42}{- 7}$

Simplify the left side.

Cancel the common factor of $- 7$ .

Cancel the common factor.

$\frac{- 7 y}{- 7} = \frac{42}{- 7}$

Divide $y$ by $1$ .

$y = \frac{42}{- 7}$

Simplify the right side.

Divide $42$ by $- 7$ .

$y = - 6$

y-intercept(s) in point form.

y-intercept(s): $(0, - 6)$

Step 3

List the intersections.

x-intercept(s): $(21, 0)$

y-intercept(s): $(0, - 6)$

Step 4

Find the x and y Intercepts 2x-7y=42

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