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The equation for line j can be written as y=-(5)/(7)x-10. Line k, which is parallel to line j, includes the point (-9,5). What is the equation of line k ? Write the equation in slope-intercept form. Write the numbers in the equation as simplified proper fractions, improper fractions, or integers.

The equation for line j j can be written as y=−57x−10 y=-\frac{5}{7} x-10 . Line k k , which is parallel to line j j , includes the point (−9,5) (-9,5) . What is the equation of line k k ?\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 j j can be written as y=−57x−10 y=-\frac{5}{7} x-10 . Line k k , which is parallel to line j j , includes the point (−9,5) (-9,5) . What is the equation of line k k ?\newlineWrite the equation in slope-intercept form. Write the numbers in the equation as simplified proper fractions, improper fractions, or integers.
  1. Identify slope of line j: Identify the slope of line j.\newlineThe equation of line j is given as y=−(57)x−10y = -\left(\frac{5}{7}\right)x - 10. The slope of line j is the coefficient of xx, which is −(57)-\left(\frac{5}{7}\right).
  2. Determine slope of line kk: Determine the slope of line kk.\newlineSince line kk is parallel to line jj, it will have the same slope. Therefore, the slope of line kk is also −(57)-\left(\frac{5}{7}\right).
  3. Use point-slope form: Use the point-slope form to write the equation of line kk. 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 −57-\frac{5}{7} and the point is (−9,5)(-9, 5).
  4. Substitute slope and point: Substitute the slope and point into the point-slope form.\newlineSubstituting m=−57m = -\frac{5}{7}, x1=−9x_1 = -9, and y1=5y_1 = 5 into the point-slope form, we get:\newliney−5=−57(x−(−9))y - 5 = -\frac{5}{7}(x - (-9))\newliney−5=−57(x+9)y - 5 = -\frac{5}{7}(x + 9)
  5. Distribute slope and simplify: Distribute the slope and simplify the equation.\newlineDistribute −(57) -(\frac{5}{7}) across (x+9) (x + 9) :\newliney−5=−(57)x−(57)(9) y - 5 = -(\frac{5}{7})x - (\frac{5}{7})(9) \newliney−5=−(57)x−457 y - 5 = -(\frac{5}{7})x - \frac{45}{7}
  6. Solve for y: Solve for y to write the equation in slope-intercept form.\newlineAdd 55 to both sides of the equation to isolate yy:\newliney=−57x−457+5y = -\frac{5}{7}x - \frac{45}{7} + 5\newliney=−57x−457+357y = -\frac{5}{7}x - \frac{45}{7} + \frac{35}{7}\newliney=−57x−107y = -\frac{5}{7}x - \frac{10}{7}

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