Find the Slope and y-intercept (4,3) , (7,12)

$(4, 3)$ , $(7, 12)$

Step 1

Find the value of the slope.

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

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

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).

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

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

$m = \frac{12 - (3)}{7 - (4)}$

Simplify.

Simplify the numerator.

Multiply $- 1$ by $3$ .

$m = \frac{12 - 3}{7 - (4)}$

Subtract $3$ from $12$ .

$m = \frac{9}{7 - (4)}$

Simplify the denominator.

Multiply $- 1$ by $4$ .

$m = \frac{9}{7 - 4}$

Subtract $4$ from $7$ .

$m = \frac{9}{3}$

Divide $9$ by $3$ .

$m = 3$

Step 2

Find the value of the y-intercept.

Substitute the value of $m$ into the slope-intercept form of the equation, $y = m x + b$ .

$y = (3) \cdot x + b$

Substitute the value of $x$ into the slope-intercept form of the equation, $y = m x + b$ .

$y = (3) \cdot (4) + b$

Substitute the value of $y$ into the slope-intercept form of the equation, $y = m x + b$ .

$3 = (3) \cdot (4) + b$

Rewrite the equation as $(3) \cdot (4) + b = 3$ .

$(3) \cdot (4) + b = 3$

Multiply $3$ by $4$ .

$12 + b = 3$

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

Subtract $12$ from both sides of the equation.

$b = 3 - 12$

Subtract $12$ from $3$ .

$b = - 9$

Step 3

List the slope and y-intercept.

Slope: $3$

y-intercept: $(0, - 9)$

Step 4

Find the Slope and y-intercept (4,3) , (7,12)

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