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: [tex]y=kx[/tex], where k= constant of variation.
Slope intercept equation of line is in form: [tex]y=mx+b[/tex], 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.
[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]
[tex]m=\frac{3-0}{1-0}[/tex]
[tex]m=\frac{3}{1}=3[/tex]
Upon substituting m=3 and b=0 in slope intercept form of equation we will get: [tex]y=3x+0[/tex]. Upon comparing our line with direct variation equation we can see that k=3, therefore, option a is the correct choice.
