the function that has an x-intercept of -2 and a y-intercept of −(2/3)

Question
Functions
asked 2021-01-10
the function that has an x-intercept of -2 and a y-intercept of \(\displaystyle−{\left(\frac{{2}}{{3}}\right)}\)

Answers (1)

2021-01-11
Use the slope-intercept form of a line:
y=mx+b
The xx-intercept represents point (−2,0) so by substitution,
0=m(−2)+b
2m=b(1)
The yy-intercept represents point (0,−(2/3)) so by substitution, -(2/3)=m(0)+b
-(2/3)=b
Solve for m by substituting (2) to (1): \(\displaystyle{2}{m}=-{\left(\frac{{2}}{{3}}\right)}\)
\(\displaystyle{m}=-{\left(\frac{{1}}{{3}}\right)}\)
Hence, the function is: \(\displaystyle{y}=-{\left(\frac{{1}}{{3}}\right)}{x}-{\left(\frac{{2}}{{3}}\right)}\)
or
\(\displaystyle{f{{\left({x}\right)}}}=-{\left(\frac{{1}}{{3}}\right)}{x}-{\left(\frac{{2}}{{3}}\right)}\)
0

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