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Complete the point-slope equation of the line through (-4,8) and (4,4). Use exact numbers.

Complete the point-slope equation of the line through (−4,8)(-4,8) and (4,4)(4,4). Use exact numbers.

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Full solution

Q. Complete the point-slope equation of the line through (−4,8)(-4,8) and (4,4)(4,4). Use exact numbers.
  1. Calculate Slope: Calculate the slope of the line using the given points (−4,8)(-4,8) and (4,4)(4,4).Slope (m)=y2−y1x2−x1\text{Slope } (m) = \frac{y_2 - y_1}{x_2 - x_1}=4−84−(−4)= \frac{4 - 8}{4 - (-4)}=−48= \frac{-4}{8}=−12= -\frac{1}{2}
  2. Choose Point: Choose one of the given points to use in the point-slope form equation. We can use either point, but for this example, let's use the point (−4,8)(-4,8).
  3. Write Equation: Write the point-slope form of the equation using the slope calculated in step 11 and the point chosen in step 22.\newlineThe point-slope form is: y−y1=m(x−x1)y - y_1 = m(x - x_1)\newlineUsing the point (−4,8)(-4,8) and the slope −12-\frac{1}{2}, the equation becomes:\newliney−8=(−12)(x−(−4))y - 8 = \left(-\frac{1}{2}\right)(x - (-4))
  4. Simplify Equation: Simplify the equation by distributing the slope on the right side of the equation.\newliney−8=(−12)(x+4)y - 8 = (-\frac{1}{2})(x + 4)
  5. Final Equation: The equation is now in point-slope form and can be left as is, since the problem asks for the point-slope equation.

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