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Q25.

Expert-verifiedFound in: Page 105

Book edition
Middle English Edition

Author(s)
Carter

Pages
804 pages

ISBN
9780079039903

**Graph the line passing through the given point with the given slope**

**$25.\u200a\u200a\text{(3,-2),undefined}$**

The graph of the line passing through the point $(3,-2)$ with the undefined slope is

The slope of a line is the ratio of the change in the *y*-coordinates to the change in the *x*- coordinates.

Symbolically, the slope *m* of the line passing through the points $\left({x}_{1},{y}_{1}\right)\text{and}\left({x}_{2},{y}_{2}\right)$ is given by $m=\frac{{y}_{2}-{y}_{1}}{{x}_{2}-{x}_{1}}$ where ${x}_{1}\ne {x}_{2}$.

The given ordered pair is $\left(3,-2\right)$

Hence plot the point in the graph such that the point is 3 unit in the positive *x-*axis and 2 units in the negative *y-*axis.

Therefore, the point $\left(3,-2\right)$ in the graph is as shown below:

Given that the slope is undefined.

Slope is said to be undefined only when the denominator in $m=\frac{{y}_{2}-{y}_{1}}{{x}_{2}-{x}_{1}}$ is zero (i.e) only when ${x}_{2}-{x}_{1}=0\Rightarrow {x}_{2}={x}_{1}$. If a slope is undefined then the line will be vertical and hence the line passes through the same value of *x *and different values of *y*. That is the value of *x* remains 3 through the line.

Draw a line passing through the point $\left(3,-2\right)\text{}$and parallel to $x=3$.

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