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Write the equation of the line that passes through the points (2,-4) and (-1,-5). Put your answer in fully simplified point-slope form, unless it is a vertical or horizontal line. Answer:

Write the equation of the line that passes through the points (2,−4) (2,-4) and (−1,−5) (-1,-5) . Put your answer in fully simplified point-slope form, unless it is a vertical or horizontal line.\newlineAnswer:

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Full solution

Q. Write the equation of the line that passes through the points (2,−4) (2,-4) and (−1,−5) (-1,-5) . Put your answer in fully simplified point-slope form, unless it is a vertical or horizontal line.\newlineAnswer:
  1. Calculate Slope: First, we need to find the slope of the line that passes through the points (2,−4)(2, -4) and (−1,−5)(-1, -5). The slope formula is m=y2−y1x2−x1m = \frac{y_2 - y_1}{x_2 - x_1}.\newlineLet's calculate the slope:\newlinem=(−5−(−4))(−1−2)m = \frac{(-5 - (-4))}{(-1 - 2)}\newlinem=(−5+4)(−1−2)m = \frac{(-5 + 4)}{(-1 - 2)}\newlinem=(−1)(−3)m = \frac{(-1)}{(-3)}\newlinem=13m = \frac{1}{3}
  2. Write Equation in Point-Slope Form: Now that we have the slope, we can use one of the points and the slope to write the equation in point-slope form, which is y−y1=m(x−x1)y - y_1 = m(x - x_1). We can use the point (2,−4)(2, -4). Let's substitute the values into the point-slope form: y−(−4)=13(x−2)y - (-4) = \frac{1}{3}(x - 2) y+4=13(x−2)y + 4 = \frac{1}{3}(x - 2)
  3. Check for Further Simplification: We have the equation in point-slope form. However, we should check if it can be simplified further. Since the slope is already in simplest form and the equation is in the correct format, no further simplification is needed.

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