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The equation for line gg can be written as y=72x+6y = \frac{7}{2}x + 6. Line hh includes the point (−2,−3)(-2,-3) and is parallel to line gg. What is the equation of line hh?\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 gg can be written as y=72x+6y = \frac{7}{2}x + 6. Line hh includes the point (−2,−3)(-2,-3) and is parallel to line gg. What is the equation of line hh?\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 g: Determine the slope of line gg.\newlineLine gg has the equation y=72x+6y = \frac{7}{2}x + 6. The slope of line gg is the coefficient of xx, which is 72\frac{7}{2}.
  2. Determine slope of line hh: Since line hh is parallel to line gg, it must have the same slope. The slope of line hh is therefore also 72\frac{7}{2}.
  3. Use point-slope form: Use the point-slope form to find the equation of line hh. 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,−3)(-2, -3) and the slope 72\frac{7}{2}.
  4. Plug slope and point: Plug the slope and the point into the point-slope form.\newlineUsing the point (−2,−3)(-2, -3) and the slope 72\frac{7}{2}, we get:\newliney−(−3)=72(x−(−2))y - (-3) = \frac{7}{2}(x - (-2))\newliney+3=72(x+2)y + 3 = \frac{7}{2}(x + 2)
  5. Distribute slope: Distribute the slope on the right side of the equation.\newliney+3=72×x+72×2y + 3 = \frac{7}{2} \times x + \frac{7}{2} \times 2\newliney+3=72×x+7y + 3 = \frac{7}{2} \times x + 7
  6. Isolate y: Isolate y to get the equation in slope-intercept form.\newlineSubtract 33 from both sides of the equation:\newliney=72×x+7−3y = \frac{7}{2} \times x + 7 - 3\newliney=72×x+4y = \frac{7}{2} \times x + 4

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