Graph y=3cos(pi)(x+1/2)

$y = 3 \cos (π) (x + \frac{1}{2})$

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

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

$y = m x + b$

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

$m = - 3$

$b = - \frac{3}{2}$

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

Slope: $- 3$

y-intercept: $(0, - \frac{3}{2})$

Slope: $- 3$

y-intercept: $(0, - \frac{3}{2})$

Any line can be graphed using two points. Select two $x$ values, and plug them into the equation to find the corresponding $y$ values.

Find the x-intercept.

To find the x-intercept(s), substitute in $0$ for $y$ and solve for $x$ .

$0 = - 3 x - \frac{3}{2}$

Solve the equation.

Rewrite the equation as $- 3 x - \frac{3}{2} = 0$ .

$- 3 x - \frac{3}{2} = 0$

Add $\frac{3}{2}$ to both sides of the equation.

$- 3 x = \frac{3}{2}$

Divide each term in $- 3 x = \frac{3}{2}$ by $- 3$ and simplify.

Divide each term in $- 3 x = \frac{3}{2}$ by $- 3$ .

$\frac{- 3 x}{- 3} = \frac{\frac{3}{2}}{- 3}$

Simplify the left side.

Cancel the common factor of $- 3$ .

Cancel the common factor.

$\frac{- 3 x}{- 3} = \frac{\frac{3}{2}}{- 3}$

Divide $x$ by $1$ .

$x = \frac{\frac{3}{2}}{- 3}$

Simplify the right side.

Multiply the numerator by the reciprocal of the denominator.

$x = \frac{3}{2} \cdot \frac{1}{- 3}$

Cancel the common factor of $3$ .

Factor $3$ out of $- 3$ .

$x = \frac{3}{2} \cdot \frac{1}{3 (- 1)}$

Cancel the common factor.

$x = \frac{3}{2} \cdot \frac{1}{3 \cdot - 1}$

Rewrite the expression.

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

Multiply $\frac{1}{2}$ by $\frac{1}{- 1}$ .

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

Simplify the expression.

Multiply $2$ by $- 1$ .

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

Move the negative in front of the fraction.

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

x-intercept(s) in point form.

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

Find the y-intercept.

To find the y-intercept(s), substitute in $0$ for $x$ and solve for $y$ .

$y = - 3 \cdot 0 - \frac{3}{2}$

Solve the equation.

Remove parentheses.

$y = - 3 \cdot 0 - \frac{3}{2}$

Simplify $- 3 \cdot 0 - \frac{3}{2}$ .

Multiply $- 3$ by $0$ .

$y = 0 - \frac{3}{2}$

Subtract $\frac{3}{2}$ from $0$ .

$y = - \frac{3}{2}$

y-intercept(s) in point form.

y-intercept(s): $(0, - \frac{3}{2})$

Create a table of the $x$ and $y$ values.

$\begin{array}{c} x & y \\ - \frac{1}{2} & 0 \\ 0 & - \frac{3}{2} \end{array}$

Graph the line using the slope and the y-intercept, or the points.

Slope: $- 3$

y-intercept: $(0, - \frac{3}{2})$

$\begin{array}{c} x & y \\ - \frac{1}{2} & 0 \\ 0 & - \frac{3}{2} \end{array}$

Graph y=3cos(pi)(x+1/2)

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