Chapter 4: Q. 132 (page 534)

Find an equation of a line perpendicular to the line $y = \frac{1}{2} x - 3$ that contains the point $(6, 4)$ .

Short Answer

Expert verified

The equation of the line is $y = - 2 x + 16$ .

Step by step solution

Step 1. Given Information.

Equation of the line, $y = \frac{1}{2} x - 3$

Point, $(6, 4)$

Step 2. Finding the slope

The slope-intercept form is,

$y = m x + b$

Comparing the equation of the line $y = \frac{1}{2} x - 3$ ,

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

When two lines are perpendicular to each other,

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

Step 3. Equation of the line.

The point-slope form is,

$(y - y_{1}) = m (x - x_{1})$

Inputting the values,

$(y - 4) = - 2 (x - 6) y - 4 = - 2 x + 12 y = - 2 x + 16$

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Find an equation of a line perpendicular to the line $y = \frac{1}{2} x - 3$ that contains the point $(6, 4)$ .

Short Answer

Step by step solution

Step 1. Given Information.

Step 2. Finding the slope

Step 3. Equation of the line.

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Find an equation of a line perpendicular to the line y=12x-3that contains the point (6,4).

Short Answer

Step by step solution

Step 1. Given Information.

Step 2. Finding the slope

Step 3. Equation of the line.

One App. One Place for Learning.

Most popular questions from this chapter

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Theoretical and Mathematical Physics

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Study anywhere. Anytime. Across all devices.

Find an equation of a line perpendicular to the line $y = \frac{1}{2} x - 3$ that contains the point $(6, 4)$ .