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Line cc has an equation of y=−34x−3y = -\frac{3}{4}x - 3. Line dd, which is parallel to line cc, includes the point (−2,−2)(-2,-2). What is the equation of line dd?\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. Line cc has an equation of y=−34x−3y = -\frac{3}{4}x - 3. Line dd, which is parallel to line cc, includes the point (−2,−2)(-2,-2). What is the equation of line dd?\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 c: Determine the slope of line c. Line c has an equation of y=−34x−3y = -\frac{3}{4}x - 3. The slope of a line in the form y=mx+by = mx + b is mm, where mm is the coefficient of xx. The slope of line c is −34-\frac{3}{4}.
  2. Determine Slope of Line dd: Since line dd is parallel to line cc, it must have the same slope. The slope of line dd is therefore also −34-\frac{3}{4}.
  3. Use Point-Slope Form: Use the point-slope form to find the equation of line dd. 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 have the point (−2,−2)(-2, -2) and the slope −34-\frac{3}{4}. Plugging these into the point-slope form gives us y−(−2)=−34(x−(−2))y - (-2) = -\frac{3}{4}(x - (-2)).
  4. Convert to Slope-Intercept Form: Simplify the equation from the point-slope form to the slope-intercept form.\newliney+2=−34(x+2)y + 2 = -\frac{3}{4}(x + 2)\newliney+2=−34x−34(2)y + 2 = -\frac{3}{4}x - \frac{3}{4}(2)\newliney+2=−34x−32y + 2 = -\frac{3}{4}x - \frac{3}{2}\newlineSubtract 22 from both sides to get y by itself:\newliney=−34x−32−2y = -\frac{3}{4}x - \frac{3}{2} - 2\newliney=−34x−32−42y = -\frac{3}{4}x - \frac{3}{2} - \frac{4}{2}\newliney=−34x−72y = -\frac{3}{4}x - \frac{7}{2}

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