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The equation of line cc is y=5x−25y = 5x - \frac{2}{5}. Line dd is parallel to line cc and passes through (2,6)(2,6). What is the equation of line dd?\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 cc is y=5x−25y = 5x - \frac{2}{5}. Line dd is parallel to line cc and passes through (2,6)(2,6). What is the equation of line dd?\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 c: Determine the slope of line c. Line c has the equation y=5x−25y = 5x - \frac{2}{5}. 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 c is 55.
  2. Determine Slope of Line dd: Since line dd is parallel to line cc, it must have the same slope. Parallel lines have the same slope. Therefore, the slope of line dd is also 55.
  3. Use Point-Slope Form: Use the point-slope form to find the equation of line dd. 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 55 and the point (x1,y1)(x_1, y_1) is (2,6)(2, 6). Plugging these values into the point-slope form gives us y−6=5(x−2)y - 6 = 5(x - 2).
  4. Simplify Equation for y-Intercept: Simplify the equation to find the y-intercept bb of line dd. Expanding the equation from Step 33, we get y−6=5x−10y - 6 = 5x - 10. Adding 66 to both sides to solve for yy gives us y=5x−10+6y = 5x - 10 + 6. Simplifying the right side, we get y=5x−4y = 5x - 4.
  5. Write Final Equation: Write the final equation of line dd in slope-intercept form. The slope-intercept form is y=mx+by = mx + b, where mm is the slope and bb is the y-intercept. From Step 44, we have the slope m=5m = 5 and the y-intercept b=−4b = -4. Therefore, the equation of line dd in slope-intercept form is y=5x−4y = 5x - 4.

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