Write an equation of the line that passes through a pair of points: (-5, – 2), (4, 5)

Question

Write an equation of the line that passes through a pair of points:
(-5, – 2), (4, 5)

in progress 0
Khải Quang 4 years 2021-08-23T02:42:20+00:00 1 Answers 10 views 0

Answers ( )

  1. Euphemia
    0
    2021-08-23T02:43:55+00:00
    Reply

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

    y = \frac{7}{9} x+\frac{17}{9}

    Step-by-step explanation:

    1) First, find the slope of the line. Use 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{(5)-(-2)}{(4)-(-5)} \\m = \frac{5+2}{4+5} \\m = \frac{7}{9}

    So, the slope is \frac{7}{9}.

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

    Since m represents the slope, substitute \frac{7}{9} for it. Since x_1 and y_1 represent the x and y values of one point the line intersects, choose from any one of the given points (it doesn’t matter which one, either way the result equals the same thing) and substitute its x and y values into the formula as well. (I chose (4,5), as seen below.) From there, isolate y to place the equation in slope-intercept form (y = mx + b format) and find the following answer:

    y-(5) = \frac{7}{9} (x-(4))\\y-5 = \frac{7}{9} (x-4)\\y -5=\frac{7}{9} x-\frac{28}{9}\\y = \frac{7}{9} x-\frac{28}{9} +\frac{45}{9}\\y = \frac{7}{9} x+\frac{17}{9}

Leave an answer

Browse

Giải phương trình 1 ẩn: x + 2 - 2(x + 1) = -x . Hỏi x = ? ( )