Algebra Examples

$- 4 x + 7 = 2 y - 3$

Step 1

Rewrite in slope-intercept form.

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Step 1.1

The slope-intercept form is $y = m x + b$ , where $m$ is the slope and $b$ is the y-intercept.

$y = m x + b$

Step 1.2

Rewrite the equation as $2 y - 3 = - 4 x + 7$ .

$2 y - 3 = - 4 x + 7$

Step 1.3

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

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Step 1.3.1

Add $3$ to both sides of the equation.

$2 y = - 4 x + 7 + 3$

Step 1.3.2

Add $7$ and $3$ .

$2 y = - 4 x + 10$

Step 1.4

Divide each term in $2 y = - 4 x + 10$ by $2$ and simplify.

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Step 1.4.1

Divide each term in $2 y = - 4 x + 10$ by $2$ .

$\frac{2 y}{2} = \frac{- 4 x}{2} + \frac{10}{2}$

Step 1.4.2

Simplify the left side.

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Step 1.4.2.1

Cancel the common factor of $2$ .

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Step 1.4.2.1.1

Cancel the common factor.

$\frac{2 y}{2} = \frac{- 4 x}{2} + \frac{10}{2}$

Step 1.4.2.1.2

Divide $y$ by $1$ .

$y = \frac{- 4 x}{2} + \frac{10}{2}$

Step 1.4.3

Simplify the right side.

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Step 1.4.3.1

Simplify each term.

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Step 1.4.3.1.1

Cancel the common factor of $- 4$ and $2$ .

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Step 1.4.3.1.1.1

Factor $2$ out of $- 4 x$ .

$y = \frac{2 (- 2 x)}{2} + \frac{10}{2}$

Step 1.4.3.1.1.2

Cancel the common factors.

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Step 1.4.3.1.1.2.1

Factor $2$ out of $2$ .

$y = \frac{2 (- 2 x)}{2 (1)} + \frac{10}{2}$

Step 1.4.3.1.1.2.2

Cancel the common factor.

$y = \frac{2 (- 2 x)}{2 \cdot 1} + \frac{10}{2}$

Step 1.4.3.1.1.2.3

Rewrite the expression.

$y = \frac{- 2 x}{1} + \frac{10}{2}$

Step 1.4.3.1.1.2.4

Divide $- 2 x$ by $1$ .

$y = - 2 x + \frac{10}{2}$

Step 1.4.3.1.2

Divide $10$ by $2$ .

$y = - 2 x + 5$

Step 2

Use the slope-intercept form to find the slope and y-intercept.

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Step 2.1

Find the values of $m$ and $b$ using the form $y = m x + b$ .

$m = - 2$

$b = 5$

Step 2.2

The slope of the line is the value of $m$ , and the y-intercept is the value of $b$ .

Slope: $- 2$

y-intercept: $(0, 5)$

Slope: $- 2$

y-intercept: $(0, 5)$

Step 3