Find the Slope and y-intercept (1,1) , (7,4)

$(1, 1)$ , $(7, 4)$

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.

$m = \frac{4 - (1)}{7 - (1)}$

Simplify.

Simplify the numerator.

Multiply $- 1$ by $1$ .

$m = \frac{4 - 1}{7 - (1)}$

Subtract $1$ from $4$ .

$m = \frac{3}{7 - (1)}$

Simplify the denominator.

Multiply $- 1$ by $1$ .

$m = \frac{3}{7 - 1}$

Subtract $1$ from $7$ .

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

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 2

Find the value of the y-intercept.

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

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

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

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

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

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

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

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

Multiply $\frac{1}{2}$ by $1$ .

$\frac{1}{2} + b = 1$

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

Subtract $\frac{1}{2}$ from both sides of the equation.

$b = 1 - \frac{1}{2}$

Write $1$ as a fraction with a common denominator.

$b = \frac{2}{2} - \frac{1}{2}$

Combine the numerators over the common denominator.

$b = \frac{2 - 1}{2}$

Subtract $1$ from $2$ .

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

Step 3

List the slope and y-intercept.

Slope: $\frac{1}{2}$

y-intercept: $(0, \frac{1}{2})$

Step 4

Find the Slope and y-intercept (1,1) , (7,4)

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