Find the Equation with a Point and Slope What is the equation of the line that passes through the point (4,1) and has a slope of 5/4 ?

What is the equation of the line that passes through the point $(4, 1)$ and has a slope of $\frac{5}{4}$ ?

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

Use the formula for the equation of a line to find $b$ .

$y = m x + b$

Substitute the value of $m$ into the equation.

$y = (\frac{5}{4}) x + b$

Substitute the value of $x$ into the equation.

$y = (\frac{5}{4}) \cdot (4) + b$

Substitute the value of $y$ into the equation.

$1 = (\frac{5}{4}) \cdot (4) + b$

Find the value of $b$ .

Rewrite the equation as $\frac{5}{4} \cdot 4 + b = 1$ .

$\frac{5}{4} \cdot 4 + b = 1$

Cancel the common factor of $4$ .

Cancel the common factor.

$\frac{5}{4} \cdot 4 + b = 1$

Rewrite the expression.

$5 + b = 1$

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

Subtract $5$ from both sides of the equation.

$b = 1 - 5$

Subtract $5$ from $1$ .

$b = - 4$

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.

$y = \frac{5}{4} x - 4$