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Find the equation of the line which passes through the point (7, -14) and is parallel to the given line. Express your answer in the form ax + by = c. Simplify your answer.

Mathematics

ScanSolve AI Answer

Answer

y=−87x−6y = -\frac{8}{7}x - 6

Step-by-step solution

4 steps

  1. Find the slope of the given line.

    The given line is 8x+7y=58x + 7y = 5. To find its slope, convert it to the slope-intercept form y=mx+by = mx + b.

    8x+7y=57y=−8x+5y=−87x+578x + 7y = 5 \\ 7y = -8x + 5 \\ y = -\frac{8}{7}x + \frac{5}{7}

    The slope of the given line is m=−87m = -\frac{8}{7}.

  2. Determine the slope of the new line.

    Since the new line is parallel to the given line, it will have the same slope.
    So, the slope of the new line is mnew=−87m_{new} = -\frac{8}{7}.

  3. Use the point-slope form to find the equation of the new line.

    The new line passes through the point (x1,y1)=(7,−14)(x_1, y_1) = (7, -14) and has a slope mnew=−87m_{new} = -\frac{8}{7}. The point-slope form is y−y1=m(x−x1)y - y_1 = m(x - x_1).

    y−(−14)=−87(x−7)y+14=−87(x−7)y - (-14) = -\frac{8}{7}(x - 7) \\ y + 14 = -\frac{8}{7}(x - 7)

  4. Convert the equation to slope-intercept form (y=mx+by = mx + b) and simplify.

    Distribute the slope on the right side:

    y+14=−87x+(−87)(−7)y+14=−87x+8y + 14 = -\frac{8}{7}x + \left(-\frac{8}{7}\right)(-7) \\ y + 14 = -\frac{8}{7}x + 8

    Subtract 14 from both sides to isolate yy:

    y=−87x+8−14y=−87x−6y = -\frac{8}{7}x + 8 - 14 \\ y = -\frac{8}{7}x - 6

    The equation of the line is y=−87x−6y = -\frac{8}{7}x - 6.

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