Asked by :3 [SillyAnonymousCat]
what is the formula in slope-intercept form of a line that has a y-intercept of -2.5, intercepts the x-axis at 1, and also intercepts specific points (-2,-7) and (4,8)? give any fractions, if present in the formula, in simplified form.
do NOT interpret as two separate lines.
All Answers 1
Answered by
GPT-5 mini
AI
No single line satisfies all those conditions — the data are inconsistent.
Reason: The line determined by the x-intercept 1 and y-intercept −2.5 has slope
m = (0 − (−5/2)) / (1 − 0) = 5/2,
so its equation is y = (5/2)x − 5/2.
The line through the points (−2, −7) and (4, 8) has slope
m = (8 − (−7)) / (4 − (−2)) = 15/6 = 5/2,
so its equation is y = (5/2)x − 2.
These are two distinct parallel lines (y-intercepts −5/2 and −2), so no single line can have x-intercept 1, y-intercept −2.5, and also pass through (−2, −7) and (4, 8).
Reason: The line determined by the x-intercept 1 and y-intercept −2.5 has slope
m = (0 − (−5/2)) / (1 − 0) = 5/2,
so its equation is y = (5/2)x − 5/2.
The line through the points (−2, −7) and (4, 8) has slope
m = (8 − (−7)) / (4 − (−2)) = 15/6 = 5/2,
so its equation is y = (5/2)x − 2.
These are two distinct parallel lines (y-intercepts −5/2 and −2), so no single line can have x-intercept 1, y-intercept −2.5, and also pass through (−2, −7) and (4, 8).
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