Find the x and y Intercepts y=4x+2

$y = 4 x + 2$

Step 1

Find the x-intercepts.

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

$0 = 4 x + 2$

Solve the equation.

Rewrite the equation as $4 x + 2 = 0$ .

$4 x + 2 = 0$

Subtract $2$ from both sides of the equation.

$4 x = - 2$

Divide each term in $4 x = - 2$ by $4$ and simplify.

Divide each term in $4 x = - 2$ by $4$ .

$\frac{4 x}{4} = \frac{- 2}{4}$

Simplify the left side.

Cancel the common factor of $4$ .

Cancel the common factor.

$\frac{4 x}{4} = \frac{- 2}{4}$

Divide $x$ by $1$ .

$x = \frac{- 2}{4}$

Simplify the right side.

Cancel the common factor of $- 2$ and $4$ .

Factor $2$ out of $- 2$ .

$x = \frac{2 (- 1)}{4}$

Cancel the common factors.

Factor $2$ out of $4$ .

$x = \frac{2 \cdot - 1}{2 \cdot 2}$

Cancel the common factor.

$x = \frac{2 \cdot - 1}{2 \cdot 2}$

Rewrite the expression.

$x = \frac{- 1}{2}$

Move the negative in front of the fraction.

$x = - \frac{1}{2}$

x-intercept(s) in point form.

x-intercept(s): $(- \frac{1}{2}, 0)$

Step 2

Find the y-intercepts.

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

$y = 4 (0) + 2$

Solve the equation.

Remove parentheses.

$y = 4 (0) + 2$

Simplify $4 (0) + 2$ .

Multiply $4$ by $0$ .

$y = 0 + 2$

Add $0$ and $2$ .

$y = 2$

y-intercept(s) in point form.

y-intercept(s): $(0, 2)$

Step 3

List the intersections.

x-intercept(s): $(- \frac{1}{2}, 0)$

y-intercept(s): $(0, 2)$

Step 4

Find the x and y Intercepts y=4x+2

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