Algebra Examples

$y - 3 = 2 (x + 4)$

Step 1

Write in slope-intercept form $y = m x + b$ to identify the slope $m$ .

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Step 1.1

Solve for $y$ .

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Step 1.1.1

Simplify $2 (x + 4)$ .

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Step 1.1.1.1

Rewrite.

$y - 3 = 0 + 0 + 2 (x + 4)$

Step 1.1.1.2

Simplify by adding zeros.

$y - 3 = 2 (x + 4)$

Step 1.1.1.3

Apply the distributive property.

$y - 3 = 2 x + 2 \cdot 4$

Step 1.1.1.4

Multiply $2$ by $4$ .

$y - 3 = 2 x + 8$

Step 1.1.2

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

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Step 1.1.2.1

Add $3$ to both sides of the equation.

$y = 2 x + 8 + 3$

Step 1.1.2.2

Add $8$ and $3$ .

$y = 2 x + 11$

Step 1.2

Using slope-intercept form $y = m x + b$ , identify the slope $m$ .

$y = 2 x + 11$

$m = 2$

$y = 2 x + 11$

$m = 2$

Step 2

Pick any $x$ -value, then substitute into the equation and simplify to find a point on the line.

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Step 2.1

Substitute $1$ for $x$ .

$y = 2 \cdot 1 + 11$

Step 2.2

Multiply $2$ by $1$ .

$y = 2 + 11$

Step 2.3

Add $2$ and $11$ .

$y = 13$

Step 2.4

Since $y = 13$ when $x = 1$ , $(1, 13)$ is a point on the line.

$(1, 13)$

Step 3

Plug in the values of the found point and the value of the slope into the point-slope form $y - y_{1} = m (x - x_{1})$ .

$y - 13 = 2 (x - 1)$

Step 4