Question

Can someone help me make sense of this? I have trouble with these kind of questions

Answer 1

The two diagrams are two graphs with different gradients. The gradient of a graph is a measure of change on the y axis with respect to change on the x-axis.

Typically, a graph that goes upwards from left to right has a positive gradient and that which goes downwards from left to right has a negative gradient (this will be proven).

The steps to finding the gradient of any straight-line graph are to select two points and apply the following operation on their coordinates.

`\begin{gathered} s=(y_2-y_1)/(x_2-x_1) \\ \text{Where:} \\ P_1=(x_1,y_1) \\ P_2=(x_2,y_2) \end{gathered}`

Now, on our graphs, we will perform this operation.

Graph 1:

`\begin{gathered} P_1=(-2,0) \\ P_2=(0,2) \\ s_1=(2-0)/(0-(-2))=(2)/(2)=1 \\ \text{Equation}\colon\text{ y=x+2} \end{gathered}`

Graph 2:

`\begin{gathered} P_1=(0,4) \\ P_2=(2,0) \\ s_2=(0-4)/(2-0)=-(4)/(2)=-2_{} \\ \text{Equation: y = -2x + 4} \end{gathered}`

This further buttresses our point about what graph produces a positive gradient.

Graph 1 is such that there is an equal increase on the y-axis with respect to the x-axis

Graph 2 is such that for any increase on one axis, there is a double decrease on the other.