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Line r has an equation of y-9=3(x-10). Line s includes the point (-2,-7) and is parallel to line r. What is the equation of line s ? Write the equation in slope-intercept form. Write the numbers in the equation as simplified proper fractions, improper fractions, or integers.

Line r r has an equation of y−9=3(x−10) y-9=3(x-10) . Line s s includes the point (−2,−7) (-2,-7) and is parallel to line r r . What is the equation of line s s ?\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 r r has an equation of y−9=3(x−10) y-9=3(x-10) . Line s s includes the point (−2,−7) (-2,-7) and is parallel to line r r . What is the equation of line s s ?\newlineWrite the equation in slope-intercept form. Write the numbers in the equation as simplified proper fractions, improper fractions, or integers.
  1. Identify slope of line rr: Identify the slope of line rr from its equation.\newlineThe equation of line rr is given in point-slope form: y−9=3(x−10)y - 9 = 3(x - 10). The coefficient of (x−10)(x - 10) is the slope of line rr, which is 33.
  2. Determine slope of line ss: Determine the slope of line ss. Since line ss is parallel to line rr, it will have the same slope. Therefore, the slope of line ss is also 33.
  3. Write point-slope form: Write the point-slope form of line ss using its slope and the given point.\newlineThe point-slope form 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 the given point. Substituting the slope 33 and the point (−2,−7)(-2, -7), we get y−(−7)=3(x−(−2))y - (-7) = 3(x - (-2)).
  4. Simplify to slope-intercept form: Simplify the point-slope form to get the slope-intercept form.\newlineFirst, simplify the equation: y+7=3(x+2)y + 7 = 3(x + 2). Then distribute the slope: y+7=3x+6y + 7 = 3x + 6. Finally, isolate yy by subtracting 77 from both sides: y=3x+6−7y = 3x + 6 - 7.
  5. Find y-intercept: Complete the simplification to find the y-intercept.\newlineSubtracting 77 from 66 gives us −1-1, so the equation becomes y=3x−1y = 3x - 1.

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