Find the angle of incilination of the pq

Step-by-step explanation:

We notice that if the gradient changes, then the value of \(\theta\) also changes, therefore the angle of inclination of a line is related to its gradient. We know that gradient is the ratio of a change in the \(y\)-direction to a change in the \(x\)-direction:

\[m=\frac{\Delta y}{\Delta x}\]

From trigonometry we know that the tangent function is defined as the ratio:

\[\tan \theta = \frac{\text{opposite side}}{\text{adjacent side}}\]

And from the diagram we see that

\begin{align*} \tan \theta &= \dfrac{\Delta y}{\Delta x} \\ \therefore m &= \tan \theta \qquad \text{ for } \text{0}\text{°} \leq \theta < \text{180}\text{°} \end{align*}

Therefore the gradient of a straight line is equal to the tangent of the angle formed between the line and the positive direction of the \(x\)-axis.

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graph b

step-by-step explanation:

one solution- graph a (clear intercepting point.)

no solution- graph b (they're parallel, there will never be a point of interception.)

infinite solutions- graph c (all points intercept.)