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What is the equation of the line that passes through the point (-6,-4) and has a slope of (4)/(3) ? Answer:

What is the equation of the line that passes through the point (−6,−4) (-6,-4) and has a slope of 43 \frac{4}{3} ?\newlineAnswer:

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Full solution

Q. What is the equation of the line that passes through the point (−6,−4) (-6,-4) and has a slope of 43 \frac{4}{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 have the slope mm as 43\frac{4}{3} and a point (−6,−4)(-6,-4) that the line passes through. We can substitute these values into the slope-intercept form to solve for bb. −4=43×(−6)+b-4 = \frac{4}{3} \times (-6) + b
  3. Perform multiplication: Perform the multiplication to simplify the equation.\newline−4=−8+b-4 = -8 + b
  4. Solve for b: Solve for b by adding 88 to both sides of the equation.\newline−4+8=b-4 + 8 = b\newlineb=4b = 4
  5. Write line equation: Write the equation of the line using the slope mm and the y-intercept bb. We have m=43m = \frac{4}{3} and b=4b = 4, so the equation of the line in slope-intercept form is: y=43x+4y = \frac{4}{3}x + 4

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