Question

Which graph represents the equation y=13x−4 ?

Answer 1

Answer: The correct option is graph (A).

Step-by-step explanation: We are given to select the graph that represents the following linear equation :

`y=(1)/(3)x-4~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~(i)`

Comparing with the slope-intercept form y = mx + c of a straight line, we see that

the slope of the line (i) is
`m=(1)/(3),` and y-intercept, c = -4.

Also, we know that the slope of a line passing through the points (a, b) and (c, d) is given by

`m=(d-b)/(c-a).`

Graph (A) :

The points (0, -4) and (3, -3) lies on the line. So, its slope will be

`m=(-3-(-4))/(3-0)=(1)/(3),`

the point where the line crosses the y-axis is (0, -4).

That is, y-intercept, c = -4.

Since the slope and y-intercept of graph (A) is same as that of line (i), so this option is CORRECT.

Graph (B) :

The points (0, -2) and (3, -3) lies on the line. So, its slope will be

`m=(-3-(-2))/(3-0)=-(1)/(3),`

Since the slope of graph (B) is not same as that of line (i), so this option is NOT CORRECT.

Graph (C) :

The points (0, -4) and (-3, 3) lies on the line. So, its slope will be

`m=(3-(-4))/(-3-0)=-(7)/(3),`

Since the slope of graph (C) is not same as that of line (i), so this option is NOT CORRECT.

Graph (D) :

The points (-4, 0) and (-3, 3) lies on the line. So, its slope will be

`m=(3-0)/(-3-(-4))=(3)/(1)=3,`

Since the slope of graph (B) is not same as that of line (i), so this option is NOT CORRECT.

Thus, graph (A) is the correct option.