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 :

$y=\dfrac{1}{3}x-4~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~(i)$

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

the slope of the line (i) is $m=\dfrac{1}{3},$ 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

$m=\dfrac{d-b}{c-a}.$

Graph (A) :  

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

$m=\dfrac{-3-(-4)}{3-0}=\dfrac{1}{3},$

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

$m=\dfrac{-3-(-2)}{3-0}=-\dfrac{1}{3},$

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

$m=\dfrac{3-(-4)}{-3-0}=-\dfrac{7}{3},$

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

$m=\dfrac{3-0}{-3-(-4)}=\dfrac{3}{1}=3,$

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.

Answer 2

I believe the correct answer is the first graph.