Find the equation for the line that passes through the points ( 7 , 2 ) and ( 10 , − 6 ) . Give your answer in slope intercept form

Question

Find the equation for the line that passes through the points ( 7 , 2 ) and ( 10 , − 6 ) . Give your answer in slope intercept form

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Thu Hương 1 month 2021-08-07T20:25:28+00:00 2 Answers 3 views 0

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    0
    2021-08-07T20:26:31+00:00

    Answer:

    y  =  \frac{-8}{3}x + \frac{62}{3}

    Step-by-step explanation:

    Use slope formula.

    then substitute slope for m in y = mx + b

    pick a set of coordinates and substitute them in for x and y.

    Solve for b

    0
    2021-08-07T20:27:06+00:00

    Answer:

    y=-\frac{8}{3}x+\frac{62}{3}

    Step-by-step explanation:

    Hi there!

    Slope-intercept form: y=mx+b where m is the slope and b is the y-intercept (the value of y when x is 0)

    1) Determine the slope (m)

    m=\frac{y_2-y_1}{x_2-x_1} where two given points are (x_1,y_1) and (x_2,y_2)

    Plug in the points (7,2) and (10,-6)

    m=\frac{2-(-6)}{7-10}\\m=\frac{2+6}{7-10}\\m=\frac{8}{-3}

    Therefore, the slope of the line is -\frac{8}{3}. Plug this into y=mx+b:

    y=-\frac{8}{3}x+b

    2) Determine the y-intercept (b)

    y=-\frac{8}{3}x+b

    Plug in one of the given points and solve for b

    2=-\frac{8}{3}(7)+b\\2=-\frac{56}{3}+b

    Add \frac{56}{3} to both sides to isolate b

    2+\frac{56}{3}=-\frac{56}{3}+b+\frac{56}{3}\\\frac{62}{3}=b

    Therefore, the y-intercept is \frac{62}{3}. Plug this back into y=-\frac{8}{3}x+b:

    y=-\frac{8}{3}x+\frac{62}{3}

    I hope this helps!

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