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The equation of line vv is y=x+17y = x + \frac{1}{7}. Parallel to line vv is line ww, which passes through the point (−1,−2)(-1,-2). What is the equation of line ww?\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 vv is y=x+17y = x + \frac{1}{7}. Parallel to line vv is line ww, which passes through the point (−1,−2)(-1,-2). What is the equation of line ww?\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 vv: Determine the slope of line vv. The equation of line vv is given as y=x+17y = x + \frac{1}{7}. This is in slope-intercept form y=mx+by = mx + b, where mm is the slope and bb is the y-intercept. The slope of line vv is 11, since the coefficient of xx is 11.
  2. Find slope of line ww: Since line ww is parallel to line vv, it must have the same slope.\newlineThe slope of line ww is therefore also 11.
  3. Use point-slope form: Use the point-slope form to find the equation of line ww. 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 the slope (mm) is 11 and the point (x1,y1)(x_1, y_1) is (−1,−2)(-1, -2). Plugging these values into the point-slope form gives us y−(−2)=1(x−(−1))y - (-2) = 1(x - (-1)).
  4. Simplify equation: Simplify the equation from Step 33 to get the slope-intercept form.\newliney+2=1(x+1)y + 2 = 1(x + 1)\newliney+2=x+1y + 2 = x + 1\newlineSubtract 22 from both sides to solve for yy.\newliney=x−1y = x - 1

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