ndicate the equation of the line through (2, -4) and having slope of 3/5.

Question

ndicate the equation of the line through (2, -4) and having slope of 3/5.

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Charlie 2 weeks 2021-09-12T07:13:45+00:00 2 Answers 0

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    2021-09-12T07:15:17+00:00

    Answer:

    Point-slope form: y+4=\frac{3}{5}(x-2)

    Slope-intercept form: y=\frac{3}{5}x-\frac{26}{5}

    Standard form: 3x-5y=26

    Step-by-step explanation:

    The easiest form to use here if you know it is point-slope form.  I say this because you are given a point and the slope of the equation.

    The point-slope form is y-y_1=m(x-x_1).

    Plug in your information.

    Again you are given (x_1,y_1)=(2,-4) and m=\frac{3}{5}.

    y-y1=m(x-x_1) with the line before this one gives us:

    y-(-4)=\frac{3}{5}(x-2)

    y+4=\frac{3}{5}(x-2) This is point-slope form.

    We can rearrange it for different form.

    Another form is the slope-intercept form which is y=mx+b where m is the slope and b is the y-intercept.

    So to put y+4=\frac{3}{5}(x-2) into y=mx+b we will need to distribute and isolate y.

    I will first distribute. 3/5(x-2)=3/4 x -6/5.

    So now we have y+4=\frac{3}{5}x-\frac{6}{5}

    Subtract 4 on both sides:

    y=\frac{3}{5}x-\frac{6}{5}-4[tex]Combined the like terms:[tex]y=\frac{3}{5}x-\frac{26}{5} This is slope-intercept form.

    We can also do standard form which is ax+by=c. Usually people want a,b, and c to be integers.

    So first thing I will do is get rid of the fractions by multiplying both sides by 5.

    This gives me

    5y=5\cdot \frac{3}{5}x-5 \cdot 26/5

    5y=3x-26

    Now subtract 3x on both sides

    -3x+5y=-26

    You could also multiply both sides by -1 giving you:

    3x-5y=26

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