Algebra Examples

$y - 4 = 7 (x - 6)$

Step 1

Find the x-intercepts.

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Step 1.1

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

$(0) - 4 = 7 (x - 6)$

Step 1.2

Solve the equation.

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Step 1.2.1

Rewrite the equation as $7 (x - 6) = (0) - 4$ .

$7 (x - 6) = (0) - 4$

Step 1.2.2

Subtract $4$ from $0$ .

$7 (x - 6) = - 4$

Step 1.2.3

Divide each term in $7 (x - 6) = - 4$ by $7$ and simplify.

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Step 1.2.3.1

Divide each term in $7 (x - 6) = - 4$ by $7$ .

$\frac{7 (x - 6)}{7} = \frac{- 4}{7}$

Step 1.2.3.2

Simplify the left side.

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Step 1.2.3.2.1

Cancel the common factor of $7$ .

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Step 1.2.3.2.1.1

Cancel the common factor.

$\frac{7 (x - 6)}{7} = \frac{- 4}{7}$

Step 1.2.3.2.1.2

Divide $x - 6$ by $1$ .

$x - 6 = \frac{- 4}{7}$

Step 1.2.3.3

Simplify the right side.

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Step 1.2.3.3.1

Move the negative in front of the fraction.

$x - 6 = - \frac{4}{7}$

Step 1.2.4

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

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Step 1.2.4.1

Add $6$ to both sides of the equation.

$x = - \frac{4}{7} + 6$

Step 1.2.4.2

To write $6$ as a fraction with a common denominator, multiply by $\frac{7}{7}$ .

$x = - \frac{4}{7} + 6 \cdot \frac{7}{7}$

Step 1.2.4.3

Combine $6$ and $\frac{7}{7}$ .

$x = - \frac{4}{7} + \frac{6 \cdot 7}{7}$

Step 1.2.4.4

Combine the numerators over the common denominator.

$x = \frac{- 4 + 6 \cdot 7}{7}$

Step 1.2.4.5

Simplify the numerator.

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Step 1.2.4.5.1

Multiply $6$ by $7$ .

$x = \frac{- 4 + 42}{7}$

Step 1.2.4.5.2

Add $- 4$ and $42$ .

$x = \frac{38}{7}$

Step 1.3

x-intercept(s) in point form.

x-intercept(s): $(\frac{38}{7}, 0)$

Step 2

Find the y-intercepts.

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Step 2.1

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

$y - 4 = 7 ((0) - 6)$

Step 2.2

Solve the equation.

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Step 2.2.1

Simplify $7 ((0) - 6)$ .

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Step 2.2.1.1

Subtract $6$ from $0$ .

$y - 4 = 7 \cdot - 6$

Step 2.2.1.2

Multiply $7$ by $- 6$ .

$y - 4 = - 42$

Step 2.2.2

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

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Step 2.2.2.1

Add $4$ to both sides of the equation.

$y = - 42 + 4$

Step 2.2.2.2

Add $- 42$ and $4$ .

$y = - 38$

Step 2.3

y-intercept(s) in point form.

y-intercept(s): $(0, - 38)$

Step 3

List the intersections.

x-intercept(s): $(\frac{38}{7}, 0)$

y-intercept(s): $(0, - 38)$

Step 4