Question

The graph shows a line and two similar triangles.

Answer 1

your first option y/x=1/4 is correct

Answer 2

Answer:

Option (a) is correct.

The equation of the line is expressed using expression $\frac{y}{x}=\frac{1}{4}$

Step-by-step explanation:

Given : The graph shows a line and two similar triangles.    

We have to find the expression that finds the equation of line.

Since, given two triangles are similar.

So,  Δ ABC ≅ Δ ADE  

Thus, There corresponding sides are in same proportion.

$\frac{AC}{AD}=\frac{CB}{DE}= \frac{AB}{BE}$

Substitute, we get,

$\frac{1}{y}=\frac{4}{x}= \frac{AB}{BE}$

Rearrange, we have,

$\frac{1}{4}=\frac{y}{x}= \frac{AB}{BE}$

Also, finding slope of line AE,

Coordinate of B is (4,1) and Coordinate of A is (0,0)

Th equation of line is y = mx + c

Where, m is slope and c is x intercept

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

$m=\frac{1-0}{4-0}$

Simplify, we have,

$m=\frac{1}{4}$

And c = 0

Thus, equation of line is$y=\frac{1}{4}x$

We re-writing we get,

$\frac{y}{x}=\frac{1}{4}$

Thus, The equation of the line is expressed using expression $\frac{y}{x}=\frac{1}{4}$