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The equation for line ss can be written as y=−10x+54y= -10x+ \frac{5}{4}. Parallel to line ss is line tt, which passes through the point (−1,3)(-1,3). What is the equation of line tt?

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Q. The equation for line ss can be written as y=−10x+54y= -10x+ \frac{5}{4}. Parallel to line ss is line tt, which passes through the point (−1,3)(-1,3). What is the equation of line tt?
  1. Find Slope of Line s: Determine the slope of line s. Line s has the equation y=−10x+54y = -10x + \frac{5}{4}. The slope of a line in the form y=mx+by = mx + b is mm, where mm is the coefficient of xx. The slope of line s is −10-10.
  2. Parallel Lines Slope: Since line tt is parallel to line ss, it must have the same slope. Parallel lines have identical slopes. Therefore, the slope of line tt is also −10-10.
  3. Point-Slope Form: Use the point-slope form to find the equation of line tt. 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 −10-10 and the point (x1,y1x_1, y_1) is (−1,3)(-1, 3).
  4. Plug Slope and Point: Plug the slope and point into the point-slope form equation.\newliney−3=−10(x−(−1))y - 3 = -10(x - (-1))\newliney−3=−10(x+1)y - 3 = -10(x + 1)
  5. Distribute Slope: Distribute the slope on the right side of the equation.\newliney−3=−10x−10y - 3 = -10x - 10
  6. Isolate y: Isolate y to put the equation in slope-intercept form.\newlineAdd 33 to both sides of the equation.\newliney=−10x−10+3y = -10x - 10 + 3\newliney=−10x−7y = -10x - 7
  7. Verify Equation Form: Verify that the equation is in slope-intercept form and simplified.\newlineThe equation y=−10x−7y = -10x - 7 is in the form y=mx+by = mx + b, where mm is the slope and bb is the y-intercept.\newlineThe equation is simplified and in the correct form.

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