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Write the equation of the line that passes through the points 
(-6,6) and 
(0,9). 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 (6,6) (-6,6) and (0,9) (0,9) . Put your answer in fully simplified point-slope form, unless it is a vertical or horizontal line.\newlineAnswer:

Full solution

Q. Write the equation of the line that passes through the points (6,6) (-6,6) and (0,9) (0,9) . Put your answer in fully simplified point-slope form, unless it is a vertical or horizontal line.\newlineAnswer:
  1. Find Slope: First, we need to find the slope of the line using the two given points (6,6)(-6,6) and (0,9)(0,9). The slope mm is calculated using the formula m=y2y1x2x1m = \frac{y_2 - y_1}{x_2 - x_1}.
  2. Calculate Slope: Using the points (6,6)(-6,6) and (0,9)(0,9), we plug them into the slope formula: m=960(6)=36=12m = \frac{9 - 6}{0 - (-6)} = \frac{3}{6} = \frac{1}{2}.
  3. Write Equation: Now that we have the slope, we can use one of the points and the slope to write the equation in point-slope form. The point-slope form is yy1=m(xx1)y - y_1 = m(x - x_1), where mm is the slope and (x1,y1)(x_1, y_1) is a point on the line.
  4. Use Point and Slope: We can use the point (0,9)(0,9) and the slope 12\frac{1}{2} to write the equation. Plugging these into the point-slope form, we get y9=(12)(x0)y - 9 = \left(\frac{1}{2}\right)(x - 0).
  5. Simplify Equation: Simplifying the equation, we get y9=(12)xy - 9 = \left(\frac{1}{2}\right)x. This is the equation of the line in point-slope form.

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