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Line vv has an equation of y=−15x+9y = -\frac{1}{5}x + 9. Line ww includes the point (−10,1)(-10,1) and is parallel to line vv. What is the equation of line ww?\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. Line vv has an equation of y=−15x+9y = -\frac{1}{5}x + 9. Line ww includes the point (−10,1)(-10,1) and is parallel to line vv. What is the equation of line ww?\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 v: Determine the slope of line v. Line v has an equation of y=−15x+9y = -\frac{1}{5}x + 9. The slope-intercept form of a line is y=mx+by = mx + b, where mm is the slope and bb is the y-intercept. Therefore, the slope of line v is −15-\frac{1}{5}.
  2. Determine Parallel Slope: Since line ww is parallel to line vv, it must have the same slope. Parallel lines have the same slope. Therefore, the slope of line ww is also −15-\frac{1}{5}.
  3. Calculate Y-Intercept of Line w: Use the point (−10,1)(-10,1) and the slope −15-\frac{1}{5} to find the y-intercept (b)(b) of line w.\newlineWe can use the point-slope form of the equation of a line, which is y−y1=m(x−x1)y - y_1 = m(x - x_1), where (x1,y1)(x_1, y_1) is a point on the line and mm is the slope. Plugging in the point (−10,1)(-10,1) and the slope −15-\frac{1}{5}, we get:\newline1−y1=−15(x−(−10))1 - y_1 = -\frac{1}{5}(x - (-10))\newline1−y1=−15(x+10)1 - y_1 = -\frac{1}{5}(x + 10)\newlineNow we need to solve for −15-\frac{1}{5}00, which is the y-intercept.
  4. Solve for Y-Intercept: Solve for the y-intercept bb of line ww.1=−15(−10)+b1 = -\frac{1}{5}(-10) + b1=2+b1 = 2 + bSubtract 22 from both sides to isolate bb:1−2=b1 - 2 = b−1=b-1 = bThe y-intercept of line ww is −1-1.
  5. Write Equation of Line w: Write the equation of line w in slope-intercept form.\newlineWe have the slope m=−15m = -\frac{1}{5} and the y-intercept b=−1b = -1. The slope-intercept form is y=mx+by = mx + b. Substituting the values we have:\newliney=−15x−1y = -\frac{1}{5}x - 1\newlineThis is the equation of line w in slope-intercept form.

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