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What is the equation of the line that passes through the point (2,4) and has a slope of 3 ? Answer:

What is the equation of the line that passes through the point (2,4) (2,4) and has a slope of 33 ?\newlineAnswer:

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Q. What is the equation of the line that passes through the point (2,4) (2,4) 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 are given the slope mm as 33 and a point on the line (2,4)(2,4). We can substitute these values into the slope-intercept form to find bb. So, we have y=mx+by = mx + b, which becomes 4=3(2)+b4 = 3(2) + b.
  3. Solve for b: Solve for b.\newlineNow we calculate bb using the equation from Step 22: 4=3(2)+b4 = 3(2) + b.\newline4=6+b4 = 6 + b\newline4−6=b4 - 6 = b\newline−2=b-2 = 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=−2b = -2, we can write the equation of the line in slope-intercept form: y=3x−2y = 3x - 2.

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