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

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

Step 1

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.

$y = (1) \cdot x + b$

Substitute the value of $x$ into the equation.

$y = (1) \cdot (5) + b$

Substitute the value of $y$ into the equation.

$1 = (1) \cdot (5) + b$

Find the value of $b$ .

Rewrite the equation as $(1) \cdot (5) + b = 1$ .

$(1) \cdot (5) + b = 1$

Multiply $5$ by $1$ .

$5 + b = 1$

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 $1$ .

$b = - 4$

Step 2

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.

$y = x - 4$

Step 3