Find the Equation with a Point and Slope m=5 , (4,3)

$m = 5$ , $(4, 3)$

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.

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

Substitute the value of $x$ into the equation.

$y = (5) \cdot (4) + b$

Substitute the value of $y$ into the equation.

$3 = (5) \cdot (4) + b$

Find the value of $b$ .

Rewrite the equation as $(5) \cdot (4) + b = 3$ .

$(5) \cdot (4) + b = 3$

Multiply $5$ by $4$ .

$20 + b = 3$

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

Subtract $20$ from both sides of the equation.

$b = 3 - 20$

Subtract $20$ from $3$ .

$b = - 17$

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.

$y = 5 x - 17$

Step 3