Find the Equation Using Slope-Intercept Form (2,6) 3x+5y=1

$(2, 6)$ $3 x + 5 y = 1$

Step 1

Solve for $m$ .

Subtract $5 y$ from both sides of the equation.

$3 x = 1 - 5 y$

Divide each term in $3 x = 1 - 5 y$ by $3$ and simplify.

Divide each term in $3 x = 1 - 5 y$ by $3$ .

$\frac{3 x}{3} = \frac{1}{3} + \frac{- 5 y}{3}$

Simplify the left side.

Cancel the common factor of $3$ .

Cancel the common factor.

$\frac{3 x}{3} = \frac{1}{3} + \frac{- 5 y}{3}$

Divide $x$ by $1$ .

$x = \frac{1}{3} + \frac{- 5 y}{3}$

Simplify the right side.

Move the negative in front of the fraction.

$x = \frac{1}{3} - \frac{5 y}{3}$

Step 2

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.

$y = (\frac{1}{3} - \frac{5 y}{3}) \cdot x + b$

Substitute the value of $x$ into the equation.

$y = (\frac{1}{3} - \frac{5 y}{3}) \cdot (2) + b$

Substitute the value of $y$ into the equation.

$6 = (\frac{1}{3} - \frac{5 (6)}{3}) \cdot (2) + b$

Find the value of $b$ .

Rewrite the equation as $(\frac{1}{3} - \frac{5 (6)}{3}) \cdot 2 + b = 6$ .

$(\frac{1}{3} - \frac{5 (6)}{3}) \cdot 2 + b = 6$

Simplify each term.

Combine the numerators over the common denominator.

$\frac{1 - 5 \cdot 6}{3} \cdot 2 + b = 6$

Multiply $- 5$ by $6$ .

$\frac{1 - 30}{3} \cdot 2 + b = 6$

Subtract $30$ from $1$ .

$\frac{- 29}{3} \cdot 2 + b = 6$

Move the negative in front of the fraction.

$- \frac{29}{3} \cdot 2 + b = 6$

Multiply $- \frac{29}{3} \cdot 2$ .

Multiply $2$ by $- 1$ .

$- 2 (\frac{29}{3}) + b = 6$

Combine $- 2$ and $\frac{29}{3}$ .

$\frac{- 2 \cdot 29}{3} + b = 6$

Multiply $- 2$ by $29$ .

$\frac{- 58}{3} + b = 6$

Move the negative in front of the fraction.

$- \frac{58}{3} + b = 6$

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

Add $\frac{58}{3}$ to both sides of the equation.

$b = 6 + \frac{58}{3}$

To write $6$ as a fraction with a common denominator, multiply by $\frac{3}{3}$ .

$b = 6 \cdot \frac{3}{3} + \frac{58}{3}$

Combine $6$ and $\frac{3}{3}$ .

$b = \frac{6 \cdot 3}{3} + \frac{58}{3}$

Combine the numerators over the common denominator.

$b = \frac{6 \cdot 3 + 58}{3}$

Simplify the numerator.

Multiply $6$ by $3$ .

$b = \frac{18 + 58}{3}$

Add $18$ and $58$ .

$b = \frac{76}{3}$

Step 3

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.

$y = \frac{1}{3} x - \frac{5}{3} x y + \frac{76}{3}$

Step 4

Find the Equation Using Slope-Intercept Form (2,6) 3x+5y=1

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