a line passes through the points (-11,10) and (14,-10). write the equation in slope-intercept form

asked by guest
on Dec 08, 2023 at 12:41 am

You asked:

Find the equation of the line through \((-11, 10)\) and \((14, -10)\).

MathBot Answer:

Standard Form:

$$\begin{aligned}Ax + By + C = 0\end{aligned}$$$$\begin{aligned} \text{Slope} &= -\frac{A}{B} \\ \text{Slope} &= \frac{y_2-y_1}{x_2-x_1} \\ -\frac{A}{B} &= \frac{-10 - 10}{14 - -11} \\ -\frac{A}{B} &= \frac{-20}{25} \\ A =& 20, B = 25 \end{aligned}$$$$\begin{aligned}20x + 25y + C &= 0 \\ 20(-11) + 25(10) + C &= 0 \\ -220 + 250 + C &= 0 \\ 250 + C &= 220 \\ C &= -30 \end{aligned}$$An equation of the line in standard form is: $20 x + 25 y - 30 = 0$.

Slope-Intercept Form:

$$\begin{aligned} y = mx+b\end{aligned}$$$$\begin{aligned}\text{Slope} &= \frac{y_2-y_1}{x_2-x_1} \\ \text{Slope} &= \frac{-10 - 10}{14 - -11} \\ \text{Slope} &= - \frac{4}{5}\end{aligned}$$$$\begin{aligned}y &= - \frac{4}{5}x + b \\ 10 &= - \frac{4}{5} \times -11 + b \\ 10 &= \frac{44}{5} + b \\ b &= \frac{6}{5} \end{aligned}$$The slope-intercept form of the line is: $y = \frac{6}{5} - \frac{4 x}{5}$.

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