Find the Equation with a Point and y-intercept Write an equation of the line with a slope of 2 and y-intercept of 9

Write an equation of the line with a slope of $2$ and y-intercept of $9$

Step 1

Find the value of $m$ using the formula for the equation of a line.

$y = m x + b$

Step 2

Substitute the value of $m$ into the equation.

$y = m x + 2$

Step 3

Find the value of $m$ .

Rewrite the equation as $m x + 2 = y$ .

$m x + 2 = y$

Subtract $2$ from both sides of the equation.

$m x = y - 2$

Divide each term in $m x = y - 2$ by $x$ and simplify.

Divide each term in $m x = y - 2$ by $x$ .

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

Simplify the left side.

Cancel the common factor of $x$ .

Cancel the common factor.

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

Divide $m$ by $1$ .

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

Simplify the right side.

Move the negative in front of the fraction.

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

Step 4

Now that the values of $m$ (slope) and $b$ (y-intercept) are known, substitute them into $y = m x + b$ to find the equation of the line.

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

Step 5