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Line kk has an equation of y=103x+9y = \frac{10}{3}x + 9. Line ℓ\ell includes the point (−3,−2)(-3,-2) and is parallel to line kk. What is the equation of line ℓ\ell?\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 kk has an equation of y=103x+9y = \frac{10}{3}x + 9. Line ℓ\ell includes the point (−3,−2)(-3,-2) and is parallel to line kk. What is the equation of line ℓ\ell?\newlineWrite the equation in slope-intercept form. Write the numbers in the equation as simplified proper fractions, improper fractions, or integers.
  1. Check Parallel Lines: Line is parallel to kk.\newlineDo their slopes match?\newlineYes, parallel lines have the same slope.
  2. Find Slope of Line kk: Equation of line kk: \newliney=103x+9y = \frac{10}{3}x + 9\newlineFind the slope of line kk.\newlineCompare y=103x+9y = \frac{10}{3}x + 9 with y=mx+by = mx + b.\newlinem=103m = \frac{10}{3}\newlineSlope of line kk: 103\frac{10}{3}
  3. Find Slope of Line: Line is parallel to kk.\newlineSlope of line kk: 103\frac{10}{3}\newlineFind the slope of line .\newlineSince line is parallel to kk, its slope will be the same.\newlineSlope of line : 103\frac{10}{3}
  4. Find Y-Intercept: For line : \newlineSlope mm: 103\frac{10}{3} \newlinePoint: (−3,−2)(-3, -2) \newlinePlug these values in y=mx+by = mx + b and find the y-intercept.\newline−2=103(−3)+b-2 = \frac{10}{3}(-3) + b \newline−2=−10+b-2 = -10 + b\newlineb=−2+10b = -2 + 10\newlineb=8b = 8
  5. Find Equation of Line: For line : \newlineSlope mm: 103\frac{10}{3} \newliney-intercept bb: 88 \newlineWhat is the equation of the line in slope-intercept form?\newlineSubstitute 103\frac{10}{3} for mm and 88 for bb in y=mx+by = mx + b. \newliney=103x+8y = \frac{10}{3}x + 8

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