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Geometry \newline> E. 55 Equations of parallel and perpendicular lines VEB\newlineVideo (D)\newlineQuestions\newlineThe equation of line \newlines is \newliney=35x+25y=\frac{3}{5}x+\frac{2}{5}. Line \newlinet, which is parallel to line \newlines, includes the point \newline(2,1)(2,1). What is the equation of line \newlinet ?\newlineWrite the equation in slope-intercept form. Write the numbers in the equation as simplified proper fractions, improper fractions, or integers.\newlineSubmit\newline480480\newlineWork it out\newlineNot feeling ready yet? These can help:\newlineSlopes of parallel and perpendicular lines (8383)\newlineEquations of lines (2626)\newlineLesson: Equations of parallel and perpendicular lines

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Q. Geometry \newline> E. 55 Equations of parallel and perpendicular lines VEB\newlineVideo (D)\newlineQuestions\newlineThe equation of line \newlines is \newliney=35x+25y=\frac{3}{5}x+\frac{2}{5}. Line \newlinet, which is parallel to line \newlines, includes the point \newline(2,1)(2,1). What is the equation of line \newlinet ?\newlineWrite the equation in slope-intercept form. Write the numbers in the equation as simplified proper fractions, improper fractions, or integers.\newlineSubmit\newline480480\newlineWork it out\newlineNot feeling ready yet? These can help:\newlineSlopes of parallel and perpendicular lines (8383)\newlineEquations of lines (2626)\newlineLesson: Equations of parallel and perpendicular lines
  1. Identify slope of line ss: Identify the slope of line ss from its equation y=35x+25y = \frac{3}{5}x + \frac{2}{5}. Since line tt is parallel to line ss, it will have the same slope. The slope of line ss (and therefore line tt) is 35\frac{3}{5}.
  2. Find equation of line t: Use the point-slope form of the equation of a line to find the equation of line t.\newlineThe point-slope form 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.\newlineSubstitute m=35m = \frac{3}{5} and the point (2,1)(2, 1) into the equation.
  3. Perform substitution: Perform the substitution: y−1=(35)(x−2).y - 1 = \left(\frac{3}{5}\right)(x - 2).
  4. Distribute slope: Distribute the slope on the right side of the equation: y−1=(35)x−(35)⋅2y - 1 = \left(\frac{3}{5}\right)x - \left(\frac{3}{5}\right)\cdot 2.
  5. Simplify equation: Simplify the equation: y−1=(35)x−65.y - 1 = \left(\frac{3}{5}\right)x - \frac{6}{5}.
  6. Add 11 to solve for y: Add 11 to both sides of the equation to solve for y: y=(35)x−65+1y = \left(\frac{3}{5}\right)x - \frac{6}{5} + 1.
  7. Combine like terms: Combine like terms: y=35x−65+55y = \frac{3}{5}x - \frac{6}{5} + \frac{5}{5}.
  8. Final equation of line tt: Simplify the equation: y=35x−15y = \frac{3}{5}x - \frac{1}{5}. This is the equation of line tt in slope-intercept form.

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