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The equation of line gg is y=89x+2y = \frac{8}{9}x + 2. Line hh is parallel to line gg and passes through (9,4)(9,4). 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 of line gg is y=89x+2y = \frac{8}{9}x + 2. Line hh is parallel to line gg and passes through (9,4)(9,4). 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. Determine slope of line gg: Determine the slope of line gg.\newlineLine gg has the equation y=89x+2y = \frac{8}{9}x + 2. The slope of line gg is the coefficient of xx, which is 89\frac{8}{9}.
  2. Find slope of line hh: Since line hh is parallel to line gg, it must have the same slope.\newlineThe slope of line hh is therefore also 89\frac{8}{9}.
  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 know that line hh passes through the point (9,4)(9,4) and has a slope of 89\frac{8}{9}.
  4. Plug slope and point: Plug the slope and the point into the point-slope form.\newlineUsing the point (9,4)(9,4) and the slope 89\frac{8}{9}, the equation becomes y−4=89(x−9)y - 4 = \frac{8}{9}(x - 9).
  5. Simplify equation: Simplify the equation to get it into slope-intercept form, y=mx+by = mx + b.
    y−4=89(x−9)y - 4 = \frac{8}{9}(x - 9)
    y−4=89x−8y - 4 = \frac{8}{9}x - 8
    y=89x−8+4y = \frac{8}{9}x - 8 + 4
    y=89x−4y = \frac{8}{9}x - 4
  6. Find y-intercept: Combine like terms to find the y-intercept bb.−8+4=−4-8 + 4 = -4 So the y-intercept is −4-4.
  7. Write final equation: Write the final equation of line hh in slope-intercept form.\newlineThe equation of line hh is y=89x−4y = \frac{8}{9}x - 4.

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