Find the Slope and y-intercept g(x)=2x-(1+2x)/2

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

Step 1

Rewrite in slope-intercept form.

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

$y = m x + b$

Simplify the right side.

Simplify $2 x - \frac{1 + 2 x}{2}$ .

To write $2 x$ as a fraction with a common denominator, multiply by $\frac{2}{2}$ .

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

Simplify terms.

Combine $2 x$ and $\frac{2}{2}$ .

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

Combine the numerators over the common denominator.

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

Simplify the numerator.

Multiply $2$ by $2$ .

$y = \frac{4 x - (1 + 2 x)}{2}$

Apply the distributive property.

$y = \frac{4 x - 1 \cdot 1 - (2 x)}{2}$

Multiply $- 1$ by $1$ .

$y = \frac{4 x - 1 - (2 x)}{2}$

Multiply $2$ by $- 1$ .

$y = \frac{4 x - 1 - 2 x}{2}$

Subtract $2 x$ from $4 x$ .

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

Simplify $\frac{2 x - 1}{2}$ .

Split the fraction $\frac{2 x - 1}{2}$ into two fractions.

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

Simplify each term.

Cancel the common factor of $2$ .

Cancel the common factor.

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

Divide $x$ by $1$ .

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

Move the negative in front of the fraction.

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

Step 2

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

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

$m = 1$

$b = - \frac{1}{2}$

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

Slope: $1$

y-intercept: $(0, - \frac{1}{2})$

Slope: $1$

y-intercept: $(0, - \frac{1}{2})$

Step 3

Find the Slope and y-intercept g(x)=2x-(1+2x)/2

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