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Write the equation of the line that passes through the points
(-1,-4) and
(6,-8). Put your answer in fully simplified point-slope form, unless it is a vertical or horizontal line.
Answer:
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Write the equation of the line that passes through the points $(-1,-4)$ and $(6,-8)$ . Put your answer in fully simplified point-slope form, unless it is a vertical or horizontal line. $\newline$ Answer: $\newline$ Submit Answer

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Find the magnitude of a three-dimensional vector

Full solution

Q. Write the equation of the line that passes through the points

(-1,-4)

and

(6,-8)

. Put your answer in fully simplified point-slope form, unless it is a vertical or horizontal line.

\newline

Answer:

\newline

Submit Answer

Calculate the Slope: First, calculate the slope $m$ of the line using the formula $m = \frac{y_2 - y_1}{x_2 - x_1}$ , where $(x_1, y_1)$ and $(x_2, y_2)$ are the given points. $\newline$ $m = \frac{-8 - (-4)}{6 - (-1)}$ $\newline$ $m = \frac{-8 + 4}{6 + 1}$ $\newline$ $m = \frac{-4}{7}$
Use Point-Slope Form: Now that we have the slope, we can use the point-slope form of the line equation, which is $y - y_1 = m(x - x_1)$ . We can use either of the given points; let's use the first point $(-1, -4)$ . $\newline$ $y - (-4) = \frac{-4}{7}(x - (-1))$ $\newline$ $y + 4 = \frac{-4}{7}(x + 1)$
Simplify the Equation: Next, we simplify the equation. $\newline$ $y + 4 = \left(-\frac{4}{7}\right)x - \left(\frac{4}{7}\right)(1)$ $\newline$ $y + 4 = \left(-\frac{4}{7}\right)x - \frac{4}{7}$
Subtract to Simplify: To get the equation in point-slope form, we subtract $4$ from both sides. $\newline$ $y = \left(-\frac{4}{7}\right)x - \frac{4}{7} - 4$ $\newline$ $y = \left(-\frac{4}{7}\right)x - \frac{4}{7} - \frac{28}{7}$ $\newline$ $y = \left(-\frac{4}{7}\right)x - \frac{32}{7}$
Final Equation: The equation is now in point-slope form, and it is fully simplified.

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