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A line has a slope of 33 and passes through the point (−2,−10)(-2,-10). Write its equation in slope-intercept form.\newlineWrite your answer using integers, proper fractions, and improper fractions in simplest form.

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Full solution

Q. A line has a slope of 33 and passes through the point (−2,−10)(-2,-10). Write its equation in slope-intercept form.\newlineWrite your answer using integers, proper fractions, and improper fractions in simplest form.
  1. Remember slope-intercept form: First, remember the slope-intercept form is y=mx+by = mx + b, where mm is the slope and bb is the y-intercept.
  2. Find y-intercept: We know the slope mm is 33. Now we need to find the y-intercept bb using the point (−2,−10)(-2, -10).
  3. Plug in point: Plug the point into the equation: −10=3∗(−2)+b-10 = 3*(-2) + b.
  4. Do the math: Do the math: −10=−6+b-10 = -6 + b.
  5. Solve for b: Solve for b: b=−10+6b = -10 + 6.
  6. Final equation: So, b=−4b = -4.
  7. Final equation: So, b=−4b = -4.Now we have the slope (m=3m = 3) and the y-intercept (b=−4b = -4). The equation is y=3x−4y = 3x - 4.

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