Algebra Examples

$y + 1 = 3 (x - 4)$

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 $x$ .

$(0) + 1 = 3 (x - 4)$

Step 1.2

Solve the equation.

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Step 1.2.1

Rewrite the equation as $3 (x - 4) = (0) + 1$ .

$3 (x - 4) = (0) + 1$

Step 1.2.2

Add $0$ and $1$ .

$3 (x - 4) = 1$

Step 1.2.3

Divide each term in $3 (x - 4) = 1$ by $3$ and simplify.

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Step 1.2.3.1

Divide each term in $3 (x - 4) = 1$ by $3$ .

$\frac{3 (x - 4)}{3} = \frac{1}{3}$

Step 1.2.3.2

Simplify the left side.

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Step 1.2.3.2.1

Cancel the common factor of $3$ .

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Step 1.2.3.2.1.1

Cancel the common factor.

$\frac{3 (x - 4)}{3} = \frac{1}{3}$

Step 1.2.3.2.1.2

Divide $x - 4$ by $1$ .

$x - 4 = \frac{1}{3}$

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 $4$ to both sides of the equation.

$x = \frac{1}{3} + 4$

Step 1.2.4.2

To write $4$ as a fraction with a common denominator, multiply by $\frac{3}{3}$ .

$x = \frac{1}{3} + 4 \cdot \frac{3}{3}$

Step 1.2.4.3

Combine $4$ and $\frac{3}{3}$ .

$x = \frac{1}{3} + \frac{4 \cdot 3}{3}$

Step 1.2.4.4

Combine the numerators over the common denominator.

$x = \frac{1 + 4 \cdot 3}{3}$

Step 1.2.4.5

Simplify the numerator.

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Step 1.2.4.5.1

Multiply $4$ by $3$ .

$x = \frac{1 + 12}{3}$

Step 1.2.4.5.2

Add $1$ and $12$ .

$x = \frac{13}{3}$

Step 1.3

x-intercept(s) in point form.

x-intercept(s): $(\frac{13}{3}, 0)$

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 $y$ .

$y + 1 = 3 ((0) - 4)$

Step 2.2

Solve the equation.

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Step 2.2.1

Simplify $3 ((0) - 4)$ .

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Step 2.2.1.1

Subtract $4$ from $0$ .

$y + 1 = 3 \cdot - 4$

Step 2.2.1.2

Multiply $3$ by $- 4$ .

$y + 1 = - 12$

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

Subtract $1$ from both sides of the equation.

$y = - 12 - 1$

Step 2.2.2.2

Subtract $1$ from $- 12$ .

$y = - 13$

Step 2.3

y-intercept(s) in point form.

y-intercept(s): $(0, - 13)$

Step 3

List the intersections.

x-intercept(s): $(\frac{13}{3}, 0)$

y-intercept(s): $(0, - 13)$

Step 4