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What is the equation of the line that passes through the point (-7,3) and has a slope of -1 ? Answer:

What is the equation of the line that passes through the point (−7,3) (-7,3) and has a slope of −1-1 ?\newlineAnswer:

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Q. What is the equation of the line that passes through the point (−7,3) (-7,3) and has a slope of −1-1 ?\newlineAnswer:
  1. Identify Slope-Intercept Form: Identify the slope-intercept form of a line's equation.\newlineThe slope-intercept form of a line's equation is y=mx+by = mx + b, where mm is the slope and bb is the y-intercept.
  2. Find Y-Intercept: Use the given slope and point to find the y-intercept bb. We have the slope mm as −1-1 and a point (−7,3)(-7, 3) that the line passes through. We can substitute these values into the slope-intercept form to find bb. So, we plug in x=−7x = -7, y=3y = 3, and m=−1m = -1 into the equation y=mx+by = mx + b to get: 3=(−1)(−7)+b3 = (-1)(-7) + b
  3. Solve for b: Solve for b.\newlineNow we calculate the value of bb:\newline3=7+b3 = 7 + b\newlineTo isolate bb, we subtract 77 from both sides of the equation:\newline3−7=b3 - 7 = b\newline−4=b-4 = b
  4. Write Line Equation: Write the equation of the line using the slope and y-intercept.\newlineNow that we have the slope m=−1m = -1 and the y-intercept b=−4b = -4, we can write the equation of the line in slope-intercept form:\newliney=mx+by = mx + b\newliney=(−1)x+(−4)y = (-1)x + (-4)\newliney=−x−4y = -x - 4

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