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What is the equation of the line that passes through the point (2,5) and has a slope of 3 ? Answer:

What is the equation of the line that passes through the point (2,5) (2,5) and has a slope of 33 ?\newlineAnswer:

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Full solution

Q. What is the equation of the line that passes through the point (2,5) (2,5) and has a slope of 33 ?\newlineAnswer:
  1. Identify Equation 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 know the slope mm is 33 and the line passes through the point (2,5)(2,5). We can substitute these values into the slope-intercept form to find bb. 5=3(2)+b5 = 3(2) + b
  3. Solve for b: Solve for b.\newline5=6+b5 = 6 + b\newlineSubtract 66 from both sides to isolate b.\newline5−6=b5 - 6 = b\newline−1=b-1 = b
  4. Write Line Equation: Write the equation of the line using the slope and y-intercept.\newlineNow that we have the slope m=3m = 3 and the y-intercept b=−1b = -1, we can write the equation of the line.\newliney=3x−1y = 3x - 1

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