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What is the equation of the line that passes through the point (-3,7) and has a slope of (1)/(3) ? Answer:

What is the equation of the line that passes through the point (−3,7) (-3,7) and has a slope of 13 \frac{1}{3} ?\newlineAnswer:

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Q. What is the equation of the line that passes through the point (−3,7) (-3,7) and has a slope of 13 \frac{1}{3} ?\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 are given the slope mm as 13\frac{1}{3} and a point on the line (−3,7)(-3,7). We can plug these values into the slope-intercept form to solve for bb. 7=13(−3)+b7 = \frac{1}{3}(-3) + b
  3. Solve for bb: Perform the multiplication and solve for bb.7=13×−3+b7 = \frac{1}{3} \times -3 + b7=−1+b7 = -1 + b7+1=b7 + 1 = b8=b8 = b
  4. Write line equation: Write the equation of the line using the slope and y-intercept.\newlineNow that we have the slope mm as 13\frac{1}{3} and the y-intercept bb as 88, we can write the equation of the line.\newliney=13x+8y = \frac{1}{3}x + 8

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