Question

Which system is represented by the graph?

(a)y=3x-2
y=3x-1

(b)y=-3x-2
y=-3x=1

(c)y=1/3x-2
y=1/3x-1

(d) y=3x+2
y=3x+1

Answer 1

The system that is represented by the graph is (a)
`y=3x-2\\y=3x-1`.

Explanation:

The Slope-Intercept Form of the equation of a straight line is given by:

`y = mx + b`

the slope is given by
`m` and the y-intercept is given by
`b`.

The slope of a line is a number that measures its "steepness" and its given by:

`Slope=m=(\:change \:in \:y)/(\:change \:in \:x)=(y_2-y_1)/(x_2-x_1)`

The y-intercept is where a line crosses the y-axis of a graph (0, b).

From the graph, we can see that the y-intercept is -1 for the blue line and -2 for the orange line.

The blue line appears to go through the points (0,-1) and (1, 2) and the slope is

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

The orange line appears to go through the points (0,-2) and (1, 1) and the slope is

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

So, the system that is represented by the graph is

`y=3x-2\\y=3x-1`