Question

Which of the following graphs represents the equation y=-2x+3?

Answer 1

b.

Explanation:

Using the gradient rule m =(y2-y1)/(x2-x1)

M=(1-3)/(1-0)

M=-2

Into the general equation y=mx+c

Y=-2x+c

Put (1,1) a point on the line into the equation

1=-2(1)+c

1+2=c

3=c

General equation

Y=-2x+3

Answer 2

Graph B

Explanation:

We are given the equation
`y=-2x+3`.

The equation is in slope intercept form:
`y=mx+b`

'm' - slope

'b' - y-intercept

In the equation, 'b' is replaced by 3. This means that the line crosses the y-axis at (0,3). We can eliminate graph A and C, as their y-intercept is not equal to 3.

Now we have to find the slopes of Graphs B and D.

Slope is rise over run.
`m=(y_2-y_1)/(x_2-x_1)`

For Graph B:

We are given the points of (0,3) and (1,1).

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

Graph B's slope is -2.

For Graph D:

We are given the points of (0,3) and (2,2).

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

Graph D's slope is -1/2.

Since the slope for graph B is -2 and the y-intercept is 3, graph B should be the correct answer.