Question

Use the graph of the line to answer the questions.
What is an equation of the line in point-slope form?
How can the point-slope form be written in function notation?

Answer 1

Answer:

$y+1=\dfrac{1}{3}(x+2)$ - point-slope form

$f(x)=\dfrac{1}{3}x-\dfrac{1}{3}$ - function notation

Step-by-step explanation:

The point-slope form of an equation of a line:

$y-y_1=m(x-x_1)$

m - slope

The formula of a slope:

$m=\dfrac{y_2-y_1}{x_2-x_1}$

From the graph we have the points (-2, -1) and (1, 0).

Substitute:

$m=\dfrac{0-(-1)}{1-(-2)}=\dfrac{1}{3}$

$y-(-1)=\dfrac{1}{3}(x-(-2))$

$y+1=\dfrac{1}{3}(x+2)$ - point-slope form

$y+1=\dfrac{1}{3}(x+2)$          use the distributive property

$y+1=\dfrac{1}{3}x+\dfrac{2}{3}$           subtract 1 = 3/3 from both sides

$y=\dfrac{1}{3}x-\dfrac{1}{3}$

Answer 2

Answer:

Point slope form : $y-0=\frac{1}{3}(x-1)$

Function notation : $f(x)=\frac{1}{3}(x-1)$

Step-by-step explanation:

If a line passes through two points $(x_1,y_1)$ and $(x_2,y_2)$, then the point slope form of line is

$y-y_1=m(x-x_1)$

Where, m is slope.

$m=\frac{y_2-y_1}{x_2-x_1}$

From the given graph it is clear that he line passes through the points (-2,-1) and (1,0). Slope of the line is

$m=\frac{0-(-1)}{1-(-2)}=\frac{1}{3}$

The point is (1,0) and slope is 1/3. So, the point slope form of the line is

$y-0=\frac{1}{3}(x-1)$

$y=\frac{1}{3}(x-1)$

Therefore the point slope form is $y-0=\frac{1}{3}(x-1)$.

Replace y by f(x) to write the equation in function notation.

$f(x)=\frac{1}{3}(x-1)$

Therefore the function notation is $f(x)=\frac{1}{3}(x-1)$.