Find the Equation Using Two Points f(4)=-3 and f(0)=-2

$f (4) = - 3$ and $f (0) = - 2$

$f (4) = - 3$ , which means $(4, - 3)$ is a point on the line. $f (0) = - 2$ , which means $(0, - 2)$ is a point on the line, too.

$(4, - 3), (0, - 2)$

Find the slope of the line between $(4, - 3)$ and $(0, - 2)$ using $m = \frac{y_{2} - y_{1}}{x_{2} - x_{1}}$ , which is the change of $y$ over the change of $x$ .

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.

$m = \frac{- 2 - (- 3)}{0 - (4)}$

Simplify.

Simplify the numerator.

Multiply $- 1$ by $- 3$ .

$m = \frac{- 2 + 3}{0 - (4)}$

Add $- 2$ and $3$ .

$m = \frac{1}{0 - (4)}$

Simplify the denominator.

Multiply $- 1$ by $4$ .

$m = \frac{1}{0 - 4}$

Subtract $4$ from $0$ .

$m = \frac{1}{- 4}$

Move the negative in front of the fraction.

$m = - \frac{1}{4}$

Use the slope $- \frac{1}{4}$ and a given point $(4, - 3)$ to substitute for $x_{1}$ and $y_{1}$ in the point-slope form $y - y_{1} = m (x - x_{1})$ , which is derived from the slope equation $m = \frac{y_{2} - y_{1}}{x_{2} - x_{1}}$ .

$y - (- 3) = - \frac{1}{4} \cdot (x - (4))$

Simplify the equation and keep it in point-slope form.

$y + 3 = - \frac{1}{4} \cdot (x - 4)$

Solve for $y$ .

Simplify $- \frac{1}{4} \cdot (x - 4)$ .

Rewrite.

$y + 3 = 0 + 0 - \frac{1}{4} \cdot (x - 4)$

Simplify by adding zeros.

$y + 3 = - \frac{1}{4} \cdot (x - 4)$

Apply the distributive property.

$y + 3 = - \frac{1}{4} x - \frac{1}{4} \cdot - 4$

Combine $x$ and $\frac{1}{4}$ .

$y + 3 = - \frac{x}{4} - \frac{1}{4} \cdot - 4$

Cancel the common factor of $4$ .

Move the leading negative in $- \frac{1}{4}$ into the numerator.

$y + 3 = - \frac{x}{4} + \frac{- 1}{4} \cdot - 4$

Factor $4$ out of $- 4$ .

$y + 3 = - \frac{x}{4} + \frac{- 1}{4} \cdot (4 (- 1))$

Cancel the common factor.

$y + 3 = - \frac{x}{4} + \frac{- 1}{4} \cdot (4 \cdot - 1)$

Rewrite the expression.

$y + 3 = - \frac{x}{4} - 1 \cdot - 1$

Multiply $- 1$ by $- 1$ .

$y + 3 = - \frac{x}{4} + 1$

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

Subtract $3$ from both sides of the equation.

$y = - \frac{x}{4} + 1 - 3$

Subtract $3$ from $1$ .

$y = - \frac{x}{4} - 2$

The final answer is the equation in slope-intercept form.

$y = - \frac{1}{4} x - 2$

Replace $y$ by $f (x)$ .

$f (x) = - \frac{1}{4} x - 2$

Find the Equation Using Two Points f(4)=-3 and f(0)=-2

Related Questions

Support LCMGCF.com by disabling your adblocker.