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What is the equation of the line that passes through the point (8,3) and has a slope of (3)/(4) ? Answer:

What is the equation of the line that passes through the point (8,3) (8,3) and has a slope of 34 \frac{3}{4} ?\newlineAnswer:

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Q. What is the equation of the line that passes through the point (8,3) (8,3) and has a slope of 34 \frac{3}{4} ?\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 have the slope m=34m = \frac{3}{4} and a point (x,y)=(8,3)(x, y) = (8, 3). We can plug these values into the slope-intercept equation to solve for bb. 3=(34)⋅8+b3 = \left(\frac{3}{4}\right)\cdot 8 + b
  3. Perform Multiplication: Perform the multiplication to simplify the equation.\newline3=(34)⋅8+b3 = \left(\frac{3}{4}\right)\cdot 8 + b simplifies to 3=6+b3 = 6 + b.
  4. Subtract to Solve: Subtract 66 from both sides to solve for bb. \newline3−6=b3 - 6 = b, which simplifies to b=−3b = -3.
  5. Write Final Equation: Write the final equation of the line using the slope and y-intercept.\newlineNow that we have the slope m=34m = \frac{3}{4} and the y-intercept b=−3b = -3, we can write the equation of the line as y=34x−3y = \frac{3}{4}x - 3.

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