Find the Equation Using Slope-Intercept Form (3,7) ; slope 2/7

$(3, 7)$ ; slope $\frac{2}{7}$

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.

$y = (\frac{2}{7}) x + b$

Substitute the value of $x$ into the equation.

$y = (\frac{2}{7}) \cdot (3) + b$

Substitute the value of $y$ into the equation.

$7 = (\frac{2}{7}) \cdot (3) + b$

Find the value of $b$ .

Rewrite the equation as $\frac{2}{7} \cdot 3 + b = 7$ .

$\frac{2}{7} \cdot 3 + b = 7$

Multiply $\frac{2}{7} \cdot 3$ .

Combine $\frac{2}{7}$ and $3$ .

$\frac{2 \cdot 3}{7} + b = 7$

Multiply $2$ by $3$ .

$\frac{6}{7} + b = 7$

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

Subtract $\frac{6}{7}$ from both sides of the equation.

$b = 7 - \frac{6}{7}$

To write $7$ as a fraction with a common denominator, multiply by $\frac{7}{7}$ .

$b = 7 \cdot \frac{7}{7} - \frac{6}{7}$

Combine $7$ and $\frac{7}{7}$ .

$b = \frac{7 \cdot 7}{7} - \frac{6}{7}$

Combine the numerators over the common denominator.

$b = \frac{7 \cdot 7 - 6}{7}$

Simplify the numerator.

Multiply $7$ by $7$ .

$b = \frac{49 - 6}{7}$

Subtract $6$ from $49$ .

$b = \frac{43}{7}$

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.

$y = \frac{2}{7} x + \frac{43}{7}$

Step 3