Question

Which of the following equations represents the graph shown?

Answer 1

Answer: Last option.

Step-by-step explanation:

The equation of the line in slope-intercept form is:

$y=mx+b$

Where m is the slope and b the intersection with the y-axis.

You can observe in the graph that the line passes through the origin, then:

$b=0$

Choose two points of the line and calculate the slope with:

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

Points: (2,3) and (-2,-3)

Substitute values, then the slope is:

$m=\frac{-3-3}{-2-2}=\frac{-6}{-4}=\frac{3}{2}$

 Substituting "m" and "b" into  $y=mx+b$, you get that the equation is:

$y=\frac{3}{2}x$

This can be written as:

$f(x)=\frac{3}{2}x$

Answer 2

Answer:

f(x) = 3/2 x ⇒ 3rd answer

Step-by-step explanation:

* Lets study the figure

- The line passing through the origin

- The line passes through point (2 , 3)

- The standard form of the linear equation is:

  y = mx + c, where m is the slope of the line and c is the y-intercept

* Lets find the slope and the y-intercept

∵ The line passing through the origin

∴ c = 0

∵ m = (y2 - y1)/(x2 - x1)

- The line passes through (2 , 3) and (0 , 0)

∴ m = (0 - 3)/(0 - 2) = -3/-2 = 3/2

∴ f(x) = 3/2 x + 0 = 3/2 x

* f(x) = 3/2 x