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The equation for line ss can be written as y=−25x+4y = -\frac{2}{5}x + 4. Line tt, which is parallel to line ss, includes the point (−3,2)(-3,2). What is the equation of line tt?\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 ss can be written as y=−25x+4y = -\frac{2}{5}x + 4. Line tt, which is parallel to line ss, includes the point (−3,2)(-3,2). What is the equation of line tt?\newlineWrite the equation in slope-intercept form. Write the numbers in the equation as simplified proper fractions, improper fractions, or integers.
  1. Find slope of line ss: Determine the slope of line ss.\newlineLine ss has the equation y=−25x+4y = -\frac{2}{5}x + 4. The slope of line ss is the coefficient of xx, which is −25-\frac{2}{5}.
  2. Determine slope of line tt: Since line tt is parallel to line ss, it must have the same slope. The slope of line tt is therefore also −25-\frac{2}{5}.
  3. Use 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 have the point (−3,2)(-3,2) and the slope −25-\frac{2}{5}.
  4. Plug slope and point: Plug the slope and the point into the point-slope form equation.\newlineUsing the point (−3,2)(-3,2) and the slope −25-\frac{2}{5}, the equation becomes y−2=−25(x−(−3))y - 2 = -\frac{2}{5}(x - (-3)).
  5. Simplify to slope-intercept form: Simplify the equation to get it into slope-intercept form, y=mx+by = mx + b.\newliney−2=−25(x+3)y - 2 = -\frac{2}{5}(x + 3)\newliney−2=−25x−65y - 2 = -\frac{2}{5}x - \frac{6}{5}\newliney=−25x−65+2y = -\frac{2}{5}x - \frac{6}{5} + 2\newliney=−25x−65+105y = -\frac{2}{5}x - \frac{6}{5} + \frac{10}{5}\newliney=−25x+45y = -\frac{2}{5}x + \frac{4}{5}

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