Find the Slope and y-intercept (0,3) , (4,7)

$(0, 3)$ , $(4, 7)$

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.

$m = \frac{7 - (3)}{4 - (0)}$

Simplify.

Simplify the numerator.

Multiply $- 1$ by $3$ .

$m = \frac{7 - 3}{4 - (0)}$

Subtract $3$ from $7$ .

$m = \frac{4}{4 - (0)}$

Simplify the denominator.

Multiply $- 1$ by $0$ .

$m = \frac{4}{4 + 0}$

Add $4$ and $0$ .

$m = \frac{4}{4}$

Divide $4$ by $4$ .

$m = 1$

Step 2

Find the value of the y-intercept.

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

$y = (1) \cdot x + b$

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

$y = (1) \cdot (0) + b$

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

$3 = (1) \cdot (0) + b$

Rewrite the equation as $(1) \cdot (0) + b = 3$ .

$(1) \cdot (0) + b = 3$

Simplify $(1) \cdot (0) + b$ .

Multiply $0$ by $1$ .

$0 + b = 3$

Add $0$ and $b$ .

$b = 3$

Step 3

List the slope and y-intercept.

Slope: $1$

y-intercept: $(0, 3)$

Step 4

Find the Slope and y-intercept (0,3) , (4,7)

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