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Q25.

Expert-verified

Algebra 2

Found in: Page 105

Book edition Middle English Edition

Author(s) Carter

Pages 804 pages

ISBN 9780079039903

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Short Answer

Graph the line passing through the given point with the given slope
$25 . (3,-2),undefined$

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

See the step by step solution

Step by Step Solution

TABLE OF CONTENTS :

TABLE OF CONTENTS

Step-1 – Apply the concept of slope of a line

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 $(x_{1}, y_{1}) and (x_{2}, y_{2})$ is given by $m = \frac{y_{2} - y_{1}}{x_{2} - x_{1}}$ where $x_{1} \neq x_{2}$ .

Step-2 – Plot the given ordered pair

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

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 $(3, - 2)$ in the graph is as shown below:

Step-3 – Find a new point using the slope

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.

Step-4 – Graph the line

Draw a line passing through the point $(3, - 2)$ and parallel to $x = 3$ .

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