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The equation of line tt is y=−17x−2y = -\frac{1}{7}x - 2. Parallel to line tt is line uu, which passes through the point (7,6)(7,6). What is the equation of line uu?\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 tt is y=−17x−2y = -\frac{1}{7}x - 2. Parallel to line tt is line uu, which passes through the point (7,6)(7,6). What is the equation of line uu?\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 t: Determine the slope of line t.\newlineThe equation of line t is given as y=−17x−2y = -\frac{1}{7}x - 2. The slope-intercept form of a line is y=mx+by = mx + b, where mm is the slope and bb is the y-intercept. Comparing the given equation with the slope-intercept form, we can see that the slope (mm) of line t is −17-\frac{1}{7}.
  2. Find slope of line uu: Since line uu is parallel to line tt, it will have the same slope. Parallel lines have the same slope. Therefore, the slope of line uu will also be −17-\frac{1}{7}.
  3. Use point-slope form: Use the point-slope form to find the equation of line uu. 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 uu passes through the point (7,6)(7,6) and has a slope of −17-\frac{1}{7}. Plugging these values into the point-slope form gives us: y−6=−17(x−7)y - 6 = -\frac{1}{7}(x - 7).
  4. Simplify equation to slope-intercept form: Simplify the equation to get it into slope-intercept form. Distribute the slope on the right side of the equation: y−6=−17x+1y - 6 = -\frac{1}{7}x + 1. Now, add 66 to both sides to solve for yy: y=−17x+1+6y = -\frac{1}{7}x + 1 + 6. Combine like terms: y=−17x+7y = -\frac{1}{7}x + 7.

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