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Complete the equation of the line through $(3,-8)$ and $(6,-4)$

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Write a linear equation from two points

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Q. Complete the equation of the line through

(3,-8)

and

(6,-4)

Calculate Slope: Given points: $\newline$ $(3, -8)$ and $\newline$ $(6, -4)$ $\newline$ Find the slope of the line using the points. $\newline$ Slope, $m$ $\newline$ $= \frac{y_2 - y_1}{x_2 - x_1}$ $\newline$ $= \frac{-4 - (-8)}{6 - 3}$ $\newline$ $= \frac{4}{3}$ $\newline$ So, $m = \frac{4}{3}$
Find Y-Intercept: We have: $\newline$ m: $\frac{4}{3}$ $\newline$ Point: $(3, -8)$ $\newline$ Find the value of $b$ , the y-intercept. $\newline$ Substitute $x = 3$ , $y = -8$ , and $m = \frac{4}{3}$ in $y = mx + b$ . $\newline$ $-8 = \left(\frac{4}{3}\right)(3) + b$ $\newline$ $-8 = 4 + b$ $\newline$ $-8 - 4 = b$ $\newline$ $(3, -8)$ $0$ $\newline$ So, $(3, -8)$ $1$
Write Equation: We found: $\newline$ $m: \frac{4}{3}$ $\newline$ $b: -12$ $\newline$ Write the equation of the line in slope-intercept form. $\newline$ Substitute $m = \frac{4}{3}$ and $b = -12$ in $y = mx + b$ . $\newline$ $y = \left(\frac{4}{3}\right)x + (-12)$ $\newline$ $y = \left(\frac{4}{3}\right)x - 12$ $\newline$ Slope-intercept form: $y = \left(\frac{4}{3}\right)x - 12$

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