Algebra Examples

$y + 17 = 3 (x + 6) - 14$

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 $x$ .

$(0) + 17 = 3 (x + 6) - 14$

Step 1.2

Solve the equation.

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Step 1.2.1

Rewrite the equation as $3 (x + 6) - 14 = (0) + 17$ .

$3 (x + 6) - 14 = (0) + 17$

Step 1.2.2

Simplify $3 (x + 6) - 14$ .

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Step 1.2.2.1

Simplify each term.

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Step 1.2.2.1.1

Apply the distributive property.

$3 x + 3 \cdot 6 - 14 = (0) + 17$

Step 1.2.2.1.2

Multiply $3$ by $6$ .

$3 x + 18 - 14 = (0) + 17$

Step 1.2.2.2

Subtract $14$ from $18$ .

$3 x + 4 = (0) + 17$

Step 1.2.3

Add $0$ and $17$ .

$3 x + 4 = 17$

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

Subtract $4$ from both sides of the equation.

$3 x = 17 - 4$

Step 1.2.4.2

Subtract $4$ from $17$ .

$3 x = 13$

Step 1.2.5

Divide each term in $3 x = 13$ by $3$ and simplify.

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Step 1.2.5.1

Divide each term in $3 x = 13$ by $3$ .

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

Step 1.2.5.2

Simplify the left side.

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Step 1.2.5.2.1

Cancel the common factor of $3$ .

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Step 1.2.5.2.1.1

Cancel the common factor.

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

Step 1.2.5.2.1.2

Divide $x$ by $1$ .

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

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 $y$ .

$y + 17 = 3 ((0) + 6) - 14$

Step 2.2

Solve the equation.

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Step 2.2.1

Simplify $3 ((0) + 6) - 14$ .

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Step 2.2.1.1

Simplify each term.

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Step 2.2.1.1.1

Add $0$ and $6$ .

$y + 17 = 3 \cdot 6 - 14$

Step 2.2.1.1.2

Multiply $3$ by $6$ .

$y + 17 = 18 - 14$

Step 2.2.1.2

Subtract $14$ from $18$ .

$y + 17 = 4$

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 $17$ from both sides of the equation.

$y = 4 - 17$

Step 2.2.2.2

Subtract $17$ from $4$ .

$y = - 13$

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