Write an equation of the line that passes through (4,−1) and is parallel to the line y=3x+7. (hint: NOT y=3x-13)

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Write an equation of the line that passes through (4,−1) and is parallel to the line y=3x+7. (hint: NOT y=3x-13)

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    2021-09-10T20:25:32+00:00

    To find the equation of the line, we are going to use the point-slope form, which is listed below:

    (y - y_1) = m(x - x_1)

    • (x_1, y_1) is a point on the line
    • m is the slope of the line

    You may notice that we have a point, but no slope is given to us. However, the problem states that the line is parallel to the equation y = 3x + 7, which means that it has the same slope as this line, which is 3. (Remember that this line is set up in y = mx + b form, where m is the slope)

    Thus, we can now insert our values into the point-slope formula to find the equation of our line.

    (y + 1) = 3(x - 4)

    (y + 1) = 3x - 12

    y = 3x - 13

    The problem made it clear that it didn’t want the form y = 3x - 13, so let’s put it in standard form:

    y = 3x - 13

    3x - y = 13

    The equation of our line is \boxed{3x - y = 13}.

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