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The equation of line gg is y=6x−7y=6x-7. Line hh, which is parallel to line gg, includes the point (1,1)(1,1). What is the equation of line hh? Write the equation in slope-intercept form. Write the numbers in the equation as simplified proper fractions, improper fractions, or integers.

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Full solution

Q. The equation of line gg is y=6x−7y=6x-7. Line hh, which is parallel to line gg, includes the point (1,1)(1,1). What is the equation of line hh? Write the equation in slope-intercept form. Write the numbers in the equation as simplified proper fractions, improper fractions, or integers.
  1. Identify parallel lines: Line hh is parallel to gg, so they have the same slope.
  2. Determine point and slope: Line hh passes through the point (1,1)(1,1) and has the same slope as line gg, which is 66.
  3. Use point-slope form: Plug the slope 66 and the point (1,1)(1,1) into the equation y=mx+by=mx+b to find bb.
  4. Isolate y-intercept: Solve for bb.
  5. Calculate bb value: Subtract 66 from both sides to isolate bb.
  6. Write equation of line hh: Calculate the value of bb.
  7. Write equation of line hh: Calculate the value of bb. Write the equation of line hh using the slope 66 and y-intercept −5-5.

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