Final answer:
The slope-intercept form for the equation of the line given the point (2, -2) and slope 1/2 is y = (1/2)x - 3.
Step-by-step explanation:
The student is asking to find the slope-intercept form of the equation of a line that passes through the point (2,-2) with a slope that is the negative inverse of (-1/2), which is 1/2. The slope-intercept form of a linear equation is y = mx + b, where m represents the slope and b represents the y-intercept.
To find the y-intercept, we can substitute the given point and the slope into the slope-intercept form:
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- Start with the slope-intercept form: y = mx + b.
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- Plug in the slope (m = 1/2) and the coordinates of the point (2, -2): -2 = (1/2)(2) + b.
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- Simplify and solve for b: -2 = 1 + b, which gives us b = -3.
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- Write the final equation using the found slope and y-intercept: y = (1/2)x - 3.