Find the Equation Using Slope-Intercept Form point: (7,3) ; slope: 4/7

point: $(7, 3)$ ; slope: $\frac{4}{7}$

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.

$y = (\frac{4}{7}) x + b$

Substitute the value of $x$ into the equation.

$y = (\frac{4}{7}) \cdot (7) + b$

Substitute the value of $y$ into the equation.

$3 = (\frac{4}{7}) \cdot (7) + b$

Find the value of $b$ .

Rewrite the equation as $\frac{4}{7} \cdot 7 + b = 3$ .

$\frac{4}{7} \cdot 7 + b = 3$

Cancel the common factor of $7$ .

Cancel the common factor.

$\frac{4}{7} \cdot 7 + b = 3$

Rewrite the expression.

$4 + b = 3$

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

Subtract $4$ from both sides of the equation.

$b = 3 - 4$

Subtract $4$ from $3$ .

$b = - 1$

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.

$y = \frac{4}{7} x - 1$