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What is the equation of the line that passes through the point (5,6) and has a slope of -(2)/(5) ? Answer:

What is the equation of the line that passes through the point (5,6) (5,6) and has a slope of −25 -\frac{2}{5} ?\newlineAnswer:

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Full solution

Q. What is the equation of the line that passes through the point (5,6) (5,6) and has a slope of −25 -\frac{2}{5} ?\newlineAnswer:
  1. Identify Point-Slope Form: To find the equation of a line, we can use the point-slope form of a line, which is given by y−y1=m(x−x1)y - y_1 = m(x - x_1), where mm is the slope and (x1,y1)(x_1, y_1) is a point on the line.
  2. Substitute Values: Given the point (5,6)(5,6) and the slope m=−25m = -\frac{2}{5}, we can substitute these values into the point-slope form equation: y−6=−25(x−5)y - 6 = -\frac{2}{5}(x - 5).
  3. Distribute Slope: Now we will distribute the slope −25-\frac{2}{5} across the (x−5)(x - 5) term: y−6=−25x+25⋅5y - 6 = -\frac{2}{5}x + \frac{2}{5}\cdot 5.
  4. Simplify Equation: Simplify the equation by multiplying 25\frac{2}{5} by 55, which gives us 22: y−6=−25x+2y - 6 = -\frac{2}{5}x + 2.
  5. Isolate y: Next, we will add 66 to both sides of the equation to solve for yy: y=−25x+2+6y = -\frac{2}{5}x + 2 + 6.
  6. Combine Terms: Combine the constant terms on the right side of the equation: y=−25x+8y = -\frac{2}{5}x + 8.

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