Question

Which equations and/or functions represent the graphed line? Select three options.

Answer 1

Answer:

f(x) = 1/2x + 2

y - 3 = 1/2(x - 2)

y - 1 = 0.5(x + 2)

Step-by-step explanation:

Answer 2

Answer:

Point slope form : $y-3=\frac{1}{2}(x-2)$

Slope intercept form: $y=\frac{1}{2}(x)+2$

Standard form : $-x+2y=4$

Step-by-step explanation:

From the given graph it is clear that the line is passing through the points, (-4, 0), (-2, 1), (0, 2), and (2, 3).

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

$y-y_1=\frac{y_2-y_1}{x_2-x_1}(x-x_1)$

Let as consider any two points of the line:  (2, 3) and (0, 2).

The equation of line is

$y-3=\frac{2-3}{0-2}(x-2)$

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

The point slope form of the line is $y-3=\frac{1}{2}(x-2)$.

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

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

Add 3 on both sides.

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

$y=\frac{1}{2}(x)+2$

Therefore the slope intercept form of the line is $y=\frac{1}{2}(x)+2$.

Multiply both sides by 2.

$2y=x+4$

$-x+2y=4$

Therefore, the standard form of the line is $-x+2y=4$.