Question

A linear function has a slope of -7 /9 and a y-intercept of 3. How does this function compare to the linear function that is represented by the equation y + 11 = -7/9 (x minus 18)?

Answer 1

both functions have the same graph

Explanation:

The first function is described in terms of its slope and y-intercept, so can be written in slope-intercept form as ...

y = mx + b . . . . m = slope (-7/9); b = y-intercept (3)

y = -7/9x +3

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The second function is written in point-slope form:

y -k = m(x -h) . . . . m = slope (-7/9), point = (h, k) = (18, -11)

y +11 = -7/9(x -18)

If we rearrange the second equation to the form of the first, we get ...

y = -7/9x +14 -11 . . . . eliminate parentheses, subtract 11

y = -7/9x +3 . . . . . . . matches the equation of the first function

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Both functions describe the same relation.