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

Can Someone Help Me Make Sense Of This I Have Trouble With These Kind Of Questions class=

Sagot :

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.

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

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

Graph 1:

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

Graph 2:

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

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.