Find the equation of the line between the points (10, – 5) and ( – 2,0).

Question

Find the equation of the line between the points (10, – 5) and ( – 2,0).

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Kiệt Gia 3 years 2021-07-30T23:29:03+00:00 1 Answers 11 views 0

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    2021-07-30T23:30:22+00:00

    Answer (assuming it can be in slope-intercept form):

    y = -\frac{5}{12} x-\frac{5}{6}  

    Step-by-step explanation:

    1) First, find the slope of the line between the two points by using the slope formula, m  = \frac{y_2-y_1}{x_2-x_1}. Substitute the x and y values of the given points into the formula and solve:

    m = \frac{(0)-(-5)}{(-2)-(10)} \\m = \frac{0+5}{-2-10} \\m=\frac{5}{-12}

    Thus, the slope of the line is -\frac{5}{12}.

    2) Next, use the point-slope formula y-y_1 = m (x-x_1) to write the equation of the line in point-slope form. Substitute values for m, x_1, and y_1 in the formula.

    Since m represents the slope, substitute -\frac{5}{12} in its place. Since x_1 and y_1 represent the x and y values of one point the line intersects, choose any of the given points (it doesn’t matter which one, it will equal the same thing) and substitute its x and y values into the formula as well. (I chose (-2,0), as seen below.) Then, isolate y and expand the right side in the resulting equation to find the equation of the line in slope-intercept form:

    y-(0)=-\frac{5}{12} (x-(-2))\\y-0 = -\frac{5}{12} (x+2)\\y = -\frac{5}{12} x-\frac{5}{6}

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