Find the Equation Using Two Points (1,9) , (6,2)

$(1, 9)$ , $(6, 2)$

Step 1

Use $y = m x + b$ to calculate the equation of the line, where $m$ represents the slope and $b$ represents the y-intercept.

To calculate the equation of the line, use the $y = m x + b$ format.

Step 2

Slope is equal to the change in $y$ over the change in $x$ , or rise over run.

$m = \frac{(change in y)}{(change in x)}$

Step 3

The change in $x$ is equal to the difference in x-coordinates (also called run), and the change in $y$ is equal to the difference in y-coordinates (also called rise).

$m = \frac{y_{2} - y_{1}}{x_{2} - x_{1}}$

Step 4

Substitute in the values of $x$ and $y$ into the equation to find the slope.

$m = \frac{2 - (9)}{6 - (1)}$

Step 5

Finding the slope $m$ .

Simplify the numerator.

Multiply $- 1$ by $9$ .

$m = \frac{2 - 9}{6 - (1)}$

Subtract $9$ from $2$ .

$m = \frac{- 7}{6 - (1)}$

Simplify the denominator.

Multiply $- 1$ by $1$ .

$m = \frac{- 7}{6 - 1}$

Subtract $1$ from $6$ .

$m = \frac{- 7}{5}$

Move the negative in front of the fraction.

$m = - \frac{7}{5}$

Step 6

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.

$y = (- \frac{7}{5}) \cdot x + b$

Substitute the value of $x$ into the equation.

$y = (- \frac{7}{5}) \cdot (1) + b$

Substitute the value of $y$ into the equation.

$9 = (- \frac{7}{5}) \cdot (1) + b$

Find the value of $b$ .

Rewrite the equation as $- \frac{7}{5} \cdot 1 + b = 9$ .

$- \frac{7}{5} \cdot 1 + b = 9$

Multiply $- 1$ by $1$ .

$- \frac{7}{5} + b = 9$

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

Add $\frac{7}{5}$ to both sides of the equation.

$b = 9 + \frac{7}{5}$

To write $9$ as a fraction with a common denominator, multiply by $\frac{5}{5}$ .

$b = 9 \cdot \frac{5}{5} + \frac{7}{5}$

Combine $9$ and $\frac{5}{5}$ .

$b = \frac{9 \cdot 5}{5} + \frac{7}{5}$

Combine the numerators over the common denominator.

$b = \frac{9 \cdot 5 + 7}{5}$

Simplify the numerator.

Multiply $9$ by $5$ .

$b = \frac{45 + 7}{5}$

Add $45$ and $7$ .

$b = \frac{52}{5}$

Step 7

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.

$y = - \frac{7}{5} x + \frac{52}{5}$

Step 8

Find the Equation Using Two Points (1,9) , (6,2)

Related Questions

Support LCMGCF.com by disabling your adblocker.