Which explains whether or not the graph represents a direct variation?

Mathematics

2 answers:

Misha Larkins [42]3 years ago

6 0

Answer:

a. The graph has a constant of variation of 3, so it represents a direct variation.

Step-by-step explanation:

We have been given a graph and we are asked to find whether our given graph represents direct variation or not.

Since we know that a direct variation is an equation in slope-intercept form, which passes through origin (0,0) and constant of variation equals to the slope of the line.

Direct variation equation is in form: $y=kx$ , where k= constant of variation.

Slope intercept equation of line is in form: $y=mx+b$ , where m= slope and b= y-intercept.

Let us find equation of our given line in slope-intercept form.

We can see from our given graph that our line passes through the origin, so y-intercept (b) equals zero.

Let us find slope of our given line.

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

$m=\frac{3-0}{1-0}$

$m=\frac{3}{1}=3$

Upon substituting m=3 and b=0 in slope intercept form of equation we will get: $y=3x+0$ . Upon comparing our line with direct variation equation we can see that k=3, therefore, option a is the correct choice.