A line passes through the points (6,-6) and (9,-5). What is it’s equation in point slope form?

Question

A line passes through the points (6,-6) and (9,-5). What is it’s equation in point slope form?

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Thông Đạt 2 weeks 2021-09-02T08:39:20+00:00 1 Answers 0 views 0

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    2021-09-02T08:41:11+00:00

    Answer:

    y=\frac{1}{3}x-8

    Step-by-step explanation:

    Slope-intercept form of an equation is written as y=mx+b, where m is the slope and b is the y-intercept.

    The slope of a line that passes through the points (x_1,\: y_1) and (x_2, \: y_2) is m=\frac{\Delta y}{\Delta x}=\frac{y_2-y_1}{x_2-x_1}. Using the coordinates (6,-6) and (9,-5) as given in the problem, we have slope of this line to be:

    m=\frac{-5-(-6)}{9-6}=\frac{1}{3}.

    Now using this slope we’ve found and any point the line passes through, we can find the y-intercept of this equation:

    -6=\frac{1}{3}(6)+b, \\ b=-8

    Therefore, the equation of this line in slope-intercept form is \fbox{$y=\frac{1}{3}x-8$}.

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