Find the Equation with a Point and y-intercept 9/8 , y-7/2

$\frac{9}{8}$ , $y - \frac{7}{2}$

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

$y = m x + b$

Substitute the value of $m$ into the equation.

$y = m x + \frac{9}{8}$

Find the value of $m$ .

Rewrite the equation as $m x + \frac{9}{8} = y$ .

$m x + \frac{9}{8} = y$

Subtract $\frac{9}{8}$ from both sides of the equation.

$m x = y - \frac{9}{8}$

Divide each term in $m x = y - \frac{9}{8}$ by $x$ and simplify.

Divide each term in $m x = y - \frac{9}{8}$ by $x$ .

$\frac{m x}{x} = \frac{y}{x} + \frac{- \frac{9}{8}}{x}$

Simplify the left side.

Cancel the common factor of $x$ .

Cancel the common factor.

$\frac{m x}{x} = \frac{y}{x} + \frac{- \frac{9}{8}}{x}$

Divide $m$ by $1$ .

$m = \frac{y}{x} + \frac{- \frac{9}{8}}{x}$

Simplify the right side.

Simplify each term.

Multiply the numerator by the reciprocal of the denominator.

$m = \frac{y}{x} - \frac{9}{8} \cdot \frac{1}{x}$

Multiply $\frac{1}{x}$ by $\frac{9}{8}$ .

$m = \frac{y}{x} - \frac{9}{x \cdot 8}$

Move $8$ to the left of $x$ .

$m = \frac{y}{x} - \frac{9}{8 x}$

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.

$y = (\frac{y}{x} - \frac{9}{8 x}) x + \frac{9}{8}$