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

What is the equation of the line that passes through the point (6,−2) (6,-2) and has a slope of 56 \frac{5}{6} ?\newlineAnswer:

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Q. What is the equation of the line that passes through the point (6,−2) (6,-2) and has a slope of 56 \frac{5}{6} ?\newlineAnswer:
  1. Identify slope-intercept form: Identify the slope-intercept form of a line's equation. The 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 56\frac{5}{6} and the point (6,−2)(6, -2). We can plug these values into the slope-intercept form to solve for bb. −2=56×6+b-2 = \frac{5}{6} \times 6 + b
  3. Perform multiplication: Perform the multiplication to simplify the equation.\newline−2=56×6+b-2 = \frac{5}{6} \times 6 + b simplifies to −2=5+b-2 = 5 + b because 56×6\frac{5}{6} \times 6 equals 55.
  4. Solve for y-intercept: Solve for the y-intercept bb. Subtract 55 from both sides of the equation to isolate bb. −2−5=b-2 - 5 = b b=−7b = -7
  5. Write final equation: Write the final equation of the line using the slope and y-intercept.\newlineWe have the slope mm as 56\frac{5}{6} and the y-intercept bb as −7-7. The equation of the line in slope-intercept form is:\newliney=56x−7y = \frac{5}{6}x - 7

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