Chapter 3: Q. 5 (page 176)

Find the equation of the line perpendicular to the line y = 2x + 1 and containing the point (3, 5). Express your answer in slope–intercept form and graph the line.

Short Answer

Expert verified

The equation of line is $y = - \frac{1}{2} x + \frac{13}{2}$ .

Step by step solution

Step 1. Given information.

Find the equation of the line perpendicular to the line y = 2x + 1 and containing the point (3, 5). Express your answer in slope–intercept form and graph the line.

Step 2. Step 2. Definition.

The equation of line ( in slope - intercept form) is given by:

$y = m x + b; m \neq 0$

If two directions are vertical, their direction coefficients are inversely proportional:

$m_{2} = - \frac{1}{m_{1}}$

Step 3. Equation of line.

Slope:

There is given the equation of line $y = 2 x + 1$ , so the $m_{1} = 2$ . The line we are searching for is perpendicular to the given line.

Then $m_{2} = - \frac{1}{2}$ .

The y - intercept:

The point $(3, 5)$ is on the, because we want to find b, put the coordinates of the points inside the equation:

$y = - \frac{1}{2} x + b 5 = - \frac{1}{2} \cdot 3 + b 5 = - \frac{3}{2} + b b = 5 + \frac{3}{2} b = \frac{13}{2}$

So, the equation of line is :

$y = - \frac{1}{2} x + \frac{13}{2}$ y

Step 4. Conclusion.

The equation of line is $y = - \frac{1}{2} x + \frac{13}{2} y$ .

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Find the equation of the line perpendicular to the line y = 2x + 1 and containing the point (3, 5). Express your answer in slope–intercept form and graph the line.

Short Answer

Step by step solution

Step 1. Given information.

Step 2. Step 2. Definition.

Step 3. Equation of line.

Step 4. Conclusion.

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