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Complete the equation of the line through $(-10,3)$ and $(-8,-8)$

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Write a linear equation from two points

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Q. Complete the equation of the line through

(-10,3)

and

(-8,-8)

Calculate Slope: Given points: $\newline$ $(-10, 3)$ and $\newline$ $(-8, -8)$ $\newline$ Find the slope of the line using the points. $\newline$ Slope, $m$ $\newline$ $= \frac{y_2 - y_1}{x_2 - x_1}$ $\newline$ $= \frac{-8 - 3}{-8 - (-10)}$ $\newline$ $= \frac{-11}{2}$ $\newline$ So, $m = -\frac{11}{2}$
Find Y-Intercept: We have: $\newline$ m: $-\frac{11}{2}$ $\newline$ Point: $(-10, 3)$ $\newline$ Find the value of $b$ , the y-intercept. $\newline$ Substitute $x = -10$ , $y = 3$ , and $m = -\frac{11}{2}$ in $y = mx + b$ . $\newline$ $3 = \left(-\frac{11}{2}\right)(-10) + b$ $\newline$ $3 = 55 + b$ $\newline$ $3 - 55 = b$ $\newline$ $(-10, 3)$ $0$ $\newline$ So, $(-10, 3)$ $1$
Write Equation: We found: $\newline$ $m: -\frac{11}{2}$ $\newline$ $b: -52$ $\newline$ Write the equation of the line in slope-intercept form. $\newline$ Substitute $m = -\frac{11}{2}$ and $b = -52$ in $y = mx + b$ . $\newline$ $y = \left(-\frac{11}{2}\right)x + \left(-52\right)$ $\newline$ $y = \left(-\frac{11}{2}\right)x - 52$ $\newline$ Slope-intercept form: $y = \left(-\frac{11}{2}\right)x - 52$

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