Answer:
Point-slope form:
[tex]y-0=\frac{1}{3} (x-1)\\f(x)-0=\frac{1}{3}(x-1)[/tex]
Slope-intercept form:
[tex]y=\frac{1}{3}x-\frac{1}{3} \\f(x)=\frac{1}{3} x-\frac{1}{3}[/tex]
Step-by-step explanation:
You have points on that line at (-2, -1) and (1, 0). To find your slope using those points, use the slope formula.
[tex]\frac{y2-y1}{x2-x1} \\\\\frac{0-(-1)}{1-(-2)} \\\\\frac{0+1}{1+2} \\\\\frac{1}{3}[/tex]
Now that we have your slope, you can use your slope and one of your points to write an equation in point-slope form.
[tex]y-y1=m(x-x1)\\y-0=\frac{1}{3} (x-1)\\y=\frac{1}{3} x-\frac{1}{3}[/tex]
To put it in function notation, substitute y for f(x).
[tex]f(x)-0=\frac{1}{3} (x-1)\\f(x)=\frac{1}{3} x-\frac{1}{3}[/tex]
