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

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

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
$$\displaystyle{f{{\left({x}\right)}}}=-{\left(\frac{{1}}{{3}}\right)}{x}-{\left(\frac{{2}}{{3}}\right)}$$

### Relevant Questions

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