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What is the equation of the line that passes through the point (6,5) and has a slope of -(1)/(6) ? Answer:

What is the equation of the line that passes through the point (6,5) (6,5) and has a slope of −16 -\frac{1}{6} ?\newlineAnswer:

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Q. What is the equation of the line that passes through the point (6,5) (6,5) and has a slope of −16 -\frac{1}{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 −16-\frac{1}{6} and the point (6,5)(6,5). We can plug these values into the slope-intercept form to solve for bb. Using the point (6,5)(6,5), we substitute xx with 66 and yy with 55 in the equation mm00: mm11
  3. Simplify to solve for bb: Simplify the equation to solve for bb.5=−16×6+b5 = -\frac{1}{6} \times 6 + b simplifies to:5=−1+b5 = -1 + bNow, add 11 to both sides to solve for bb:5+1=b5 + 1 = b6=b6 = b
  4. Write line equation: Write the equation of the line using the slope and y-intercept.\newlineNow that we have the slope m=−16m = -\frac{1}{6} and the y-intercept b=6b = 6, we can write the equation of the line in slope-intercept form:\newliney=−16x+6y = -\frac{1}{6}x + 6

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