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The equation for line pp can be written as y=−54x−6y = -\frac{5}{4}x - 6. Line qq includes the point (5,−8)(5,-8) and is parallel to line pp. What is the equation of line qq?\newlineWrite the equation in slope-intercept form. Write the numbers in the equation as simplified proper fractions, improper fractions, or integers.

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Q. The equation for line pp can be written as y=−54x−6y = -\frac{5}{4}x - 6. Line qq includes the point (5,−8)(5,-8) and is parallel to line pp. What is the equation of line qq?\newlineWrite the equation in slope-intercept form. Write the numbers in the equation as simplified proper fractions, improper fractions, or integers.
  1. Find Slope of Line p: Determine the slope of line p. The equation of line p is given as y=−54x−6y = -\frac{5}{4}x - 6. The slope (mm) of a line in the slope-intercept form y=mx+by = mx + b is the coefficient of xx. Therefore, the slope of line p is −54-\frac{5}{4}.
  2. Determine Parallel Line Slope: Since line qq is parallel to line pp, it must have the same slope. Parallel lines have identical slopes. Therefore, the slope of line qq is also −54-\frac{5}{4}.
  3. Use Point-Slope Form: Use the point-slope form to find the equation of line qq. The point-slope form of a line is y−y1=m(x−x1)y - y_1 = m(x - x_1), where mm is the slope and (x1,y1)(x_1, y_1) is a point on the line. We know that line qq passes through the point (5,−8)(5, -8) and has a slope of −54-\frac{5}{4}. Plugging these values into the point-slope form gives us: y−(−8)=−54(x−5)y - (-8) = -\frac{5}{4}(x - 5)
  4. Simplify Equation to Slope-Intercept Form: Simplify the equation to get it into slope-intercept form.\newlineFirst, distribute the slope on the right side of the equation:\newliney+8=−54x+54×5y + 8 = -\frac{5}{4}x + \frac{5}{4} \times 5\newlineNow, simplify the right side:\newliney+8=−54x+254y + 8 = -\frac{5}{4}x + \frac{25}{4}\newlineNext, subtract 88 from both sides to solve for yy:\newliney=−54x+254−8y = -\frac{5}{4}x + \frac{25}{4} - 8\newlineConvert 88 to a fraction with a denominator of 44 to combine like terms:\newliney=−54x+254−324y = -\frac{5}{4}x + \frac{25}{4} - \frac{32}{4}\newlineNow, combine the constant terms:\newliney=−54x−74y = -\frac{5}{4}x - \frac{7}{4}

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