Algebra Examples

$y - 3 = \frac{1}{2} (x - 6)$

Step 1

Find the x-intercepts.

Tap for more steps...

Step 1.1

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

$(0) - 3 = \frac{1}{2} \cdot (x - 6)$

Step 1.2

Solve the equation.

Tap for more steps...

Step 1.2.1

Rewrite the equation as $\frac{1}{2} \cdot (x - 6) = (0) - 3$ .

$\frac{1}{2} \cdot (x - 6) = (0) - 3$

Step 1.2.2

Multiply both sides of the equation by $2$ .

$2 (\frac{1}{2} \cdot (x - 6)) = 2 ((0) - 3)$

Step 1.2.3

Simplify both sides of the equation.

Tap for more steps...

Step 1.2.3.1

Simplify the left side.

Tap for more steps...

Step 1.2.3.1.1

Simplify $2 (\frac{1}{2} \cdot (x - 6))$ .

Tap for more steps...

Step 1.2.3.1.1.1

Apply the distributive property.

$2 (\frac{1}{2} x + \frac{1}{2} \cdot - 6) = 2 ((0) - 3)$

Step 1.2.3.1.1.2

Combine $\frac{1}{2}$ and $x$ .

$2 (\frac{x}{2} + \frac{1}{2} \cdot - 6) = 2 ((0) - 3)$

Step 1.2.3.1.1.3

Cancel the common factor of $2$ .

Tap for more steps...

Step 1.2.3.1.1.3.1

Factor $2$ out of $- 6$ .

$2 (\frac{x}{2} + \frac{1}{2} \cdot (2 (- 3))) = 2 ((0) - 3)$

Step 1.2.3.1.1.3.2

Cancel the common factor.

$2 (\frac{x}{2} + \frac{1}{2} \cdot (2 \cdot - 3)) = 2 ((0) - 3)$

Step 1.2.3.1.1.3.3

Rewrite the expression.

$2 (\frac{x}{2} - 3) = 2 ((0) - 3)$

Step 1.2.3.1.1.4

Apply the distributive property.

$2 \frac{x}{2} + 2 \cdot - 3 = 2 ((0) - 3)$

Step 1.2.3.1.1.5

Cancel the common factor of $2$ .

Tap for more steps...

Step 1.2.3.1.1.5.1

Cancel the common factor.

$2 \frac{x}{2} + 2 \cdot - 3 = 2 ((0) - 3)$

Step 1.2.3.1.1.5.2

Rewrite the expression.

$x + 2 \cdot - 3 = 2 ((0) - 3)$

Step 1.2.3.1.1.6

Multiply $2$ by $- 3$ .

$x - 6 = 2 ((0) - 3)$

Step 1.2.3.2

Simplify the right side.

Tap for more steps...

Step 1.2.3.2.1

Simplify $2 ((0) - 3)$ .

Tap for more steps...

Step 1.2.3.2.1.1

Subtract $3$ from $0$ .

$x - 6 = 2 \cdot - 3$

Step 1.2.3.2.1.2

Multiply $2$ by $- 3$ .

$x - 6 = - 6$

Step 1.2.4

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

Tap for more steps...

Step 1.2.4.1

Add $6$ to both sides of the equation.

$x = - 6 + 6$

Step 1.2.4.2

Add $- 6$ and $6$ .

$x = 0$

Step 1.3

x-intercept(s) in point form.

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

Step 2

Find the y-intercepts.

Tap for more steps...

Step 2.1

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

$y - 3 = \frac{1}{2} \cdot ((0) - 6)$

Step 2.2

Solve the equation.

Tap for more steps...

Step 2.2.1

Simplify $\frac{1}{2} \cdot ((0) - 6)$ .

Tap for more steps...

Step 2.2.1.1

Subtract $6$ from $0$ .

$y - 3 = \frac{1}{2} \cdot - 6$

Step 2.2.1.2

Cancel the common factor of $2$ .

Tap for more steps...

Step 2.2.1.2.1

Factor $2$ out of $- 6$ .

$y - 3 = \frac{1}{2} \cdot (2 (- 3))$

Step 2.2.1.2.2

Cancel the common factor.

$y - 3 = \frac{1}{2} \cdot (2 \cdot - 3)$

Step 2.2.1.2.3

Rewrite the expression.

$y - 3 = - 3$

Step 2.2.2

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

Tap for more steps...

Step 2.2.2.1

Add $3$ to both sides of the equation.

$y = - 3 + 3$

Step 2.2.2.2

Add $- 3$ and $3$ .

$y = 0$

Step 2.3

y-intercept(s) in point form.

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

Step 3

List the intersections.

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

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

Step 4