Find the Equation Using Two Points (4,9) , (10,12)

$(4, 9)$ , $(10, 12)$

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.

$m = \frac{12 - (9)}{10 - (4)}$

Step 5

Finding the slope $m$ .

Simplify the numerator.

Multiply $- 1$ by $9$ .

$m = \frac{12 - 9}{10 - (4)}$

Subtract $9$ from $12$ .

$m = \frac{3}{10 - (4)}$

Simplify the denominator.

Multiply $- 1$ by $4$ .

$m = \frac{3}{10 - 4}$

Subtract $4$ from $10$ .

$m = \frac{3}{6}$

Cancel the common factor of $3$ and $6$ .

Factor $3$ out of $3$ .

$m = \frac{3 (1)}{6}$

Cancel the common factors.

Factor $3$ out of $6$ .

$m = \frac{3 \cdot 1}{3 \cdot 2}$

Cancel the common factor.

$m = \frac{3 \cdot 1}{3 \cdot 2}$

Rewrite the expression.

$m = \frac{1}{2}$

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.

$y = (\frac{1}{2}) x + b$

Substitute the value of $x$ into the equation.

$y = (\frac{1}{2}) \cdot (4) + b$

Substitute the value of $y$ into the equation.

$9 = (\frac{1}{2}) \cdot (4) + b$

Find the value of $b$ .

Rewrite the equation as $\frac{1}{2} \cdot 4 + b = 9$ .

$\frac{1}{2} \cdot 4 + b = 9$

Cancel the common factor of $2$ .

Factor $2$ out of $4$ .

$\frac{1}{2} \cdot (2 (2)) + b = 9$

Cancel the common factor.

$\frac{1}{2} \cdot (2 \cdot 2) + b = 9$

Rewrite the expression.

$2 + b = 9$

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

Subtract $2$ from both sides of the equation.

$b = 9 - 2$

Subtract $2$ from $9$ .

$b = 7$

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.

$y = \frac{1}{2} x + 7$

Step 8

Find the Equation Using Two Points (4,9) , (10,12)

Related Questions

Support LCMGCF.com by disabling your adblocker.