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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 equation y=mx+by = mx + b to solve for bb. 2=56×(−6)+b2 = \frac{5}{6} \times (-6) + b
  3. Perform multiplication: Perform the multiplication to simplify the equation. 2=−5+b2 = -5 + b
  4. Solve for b: Solve for b by adding 55 to both sides of the equation.2+5=b2 + 5 = bb=7b = 7
  5. Write final equation: Write the final equation of the line using the slope mm and y-intercept bb. We have mm as 56\frac{5}{6} and bb as 77, so the equation of the line in slope-intercept form is: y=56x+7y = \frac{5}{6}x + 7

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