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find an equation of the line passing through $(-3,8)$ and $(4,2)$

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Write a linear equation from two points

Full solution

Q. find an equation of the line passing through

(-3,8)

and

(4,2)

Calculate slope: Calculate the slope $m$ using the formula $m = \frac{y_2 - y_1}{x_2 - x_1}$ . $m = \frac{2 - 8}{4 - (-3)}$ $m = \frac{-6}{7}$ $m = -\frac{6}{7}$
Find y-intercept: Use one of the points and the slope to find the y-intercept ( $b$ ) using the formula $y = mx + b$ . Let's use the point $(-3,8)$ and the slope $-\frac{6}{7}$ . $8 = \left(-\frac{6}{7}\right)(-3) + b$ $8 = \frac{18}{7} + b$ To find $b$ , subtract $\frac{18}{7}$ from both sides. $b = 8 - \frac{18}{7}$ $b = \left(\frac{56}{7}\right) - \left(\frac{18}{7}\right)$ $y = mx + b$ $0$
Write equation: Write the equation of the line in slope-intercept form $y = mx + b$ using the slope and y-intercept we found. $y = \frac{-6}{7}x + \frac{38}{7}$

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\newline

\newline

\text{(A)horizontal line}

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\newline

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