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what is an equation of the line that passes through the point (−3,4)(-3,4) and its parallel to the line x−y=9x-y=9

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Q. what is an equation of the line that passes through the point (−3,4)(-3,4) and its parallel to the line x−y=9x-y=9
  1. Find Parallel Line Slope: First we gotta find the slope of the line that's parallel to x−y=9x - y = 9. Since parallel lines have the same slope, we can rewrite the given equation in slope-intercept form to find the slope.\newlinex−y=9x - y = 9\newline−y=−x+9-y = -x + 9\newliney=x−9y = x - 9\newlineSo the slope (m)(m) is 11.
  2. Point-Slope Form: Now we use the point-slope form to write the equation of the line that passes through (−3,4)(-3,4) with the slope we just found.\newlineThe point-slope form is y−y1=m(x−x1)y - y_1 = m(x - x_1), where (x1,y1)(x_1, y_1) is the point the line passes through and mm is the slope.\newlineSo we plug in m=1m = 1, x1=−3x_1 = -3, and y1=4y_1 = 4.\newliney−4=1(x−(−3))y - 4 = 1(x - (-3))\newliney−4=1(x+3)y - 4 = 1(x + 3)
  3. Simplify to Slope-Intercept: Next, we simplify the equation to get it into slope-intercept form, which is y=mx+by = mx + b. \newliney−4=x+3y - 4 = x + 3\newlineAdd 44 to both sides to isolate yy.\newliney=x+3+4y = x + 3 + 4\newliney=x+7y = x + 7

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