Q54. 54. Choose the equation of the l... [FREE SOLUTION]

Chapter 2: Q54. (page 80)

54. Choose the equation of the line through $(\frac{1}{2}, - \frac{3}{2})$ and $(- \frac{1}{2}, \frac{1}{2})$
$y = - 2 x - \frac{1}{2}$ (B) $y = - 3 x$ (C) $y = 2 x - \frac{5}{2}$ (D) $y = \frac{1}{2} x + 1$

Short Answer

Expert verified

The equation of the required straight line is $y = - 2 x - \frac{1}{2}$ . So, (A) is the correct option.

Step by step solution

– State the concept

The slope intercept form of a straight-line equation is $y = m x + c$ where $m$ is the slope and $c$ is the y-intercept.

The equation of a straight-line passing through the points $(h, k)$ and $(a, b)$ is given as $\frac{y - k}{x - h} = \frac{b - k}{a - h}$ .

– List the given data

It is given that the line passes through $(\frac{1}{2}, - \frac{3}{2})$ and $(- \frac{1}{2}, \frac{1}{2})$ .

Then, $(h, k) = (\frac{1}{2}, - \frac{3}{2})$ and $(a, b) = (- \frac{1}{2}, \frac{1}{2})$ .

– Write the equation

Put $(h, k) = (\frac{1}{2}, - \frac{3}{2})$ and $(a, b) = (- \frac{1}{2}, \frac{1}{2})$ in $\frac{y - k}{x - h} = \frac{b - k}{a - h}$ to get,

$\frac{y - (- \frac{3}{2})}{x - \frac{1}{2}} = \frac{\frac{1}{2} - (- \frac{3}{2})}{- \frac{1}{2} - \frac{1}{2}}$

$\frac{y + \frac{3}{2}}{x - \frac{1}{2}} = \frac{\frac{1}{2} + \frac{3}{2}}{- 1}$ (Simplify)

$\frac{y + \frac{3}{2}}{x - \frac{1}{2}} = \frac{2}{- 1}$ (Simplify)

$\frac{y + \frac{3}{2}}{x - \frac{1}{2}} = - 2$ (Simplify)

$\frac{y + \frac{3}{2}}{x - \frac{1}{2}} (x - \frac{1}{2}) = - 2 (x - \frac{1}{2})$ (Multiply both sides by $x 鈭� \frac{1}{2}$ )

$y + \frac{3}{2} = - 2 (x - \frac{1}{2})$ (Simplify)

$y + \frac{3}{2} = - 2 x + 1$ (Distributive property)

$y + \frac{3}{2} - \frac{3}{2} = - 2 x + 1 - \frac{3}{2}$ (Subtract $\frac{3}{2}$ from both sides)

$y = - 2 x - \frac{1}{2}$ (Simplify)

So, the required equation of the straight line is $y = - 2 x - \frac{1}{2}$ .

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54. Choose the equation of the line through $(\frac{1}{2}, - \frac{3}{2})$ and $(- \frac{1}{2}, \frac{1}{2})$
$y = - 2 x - \frac{1}{2}$ (B) $y = - 3 x$ (C) $y = 2 x - \frac{5}{2}$ (D) $y = \frac{1}{2} x + 1$

Short Answer

Step by step solution

– State the concept

– List the given data

– Write the equation

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54. Choose the equation of the line through 12,-32 and -12,12y=-2x-12 (B) y=-3x(C) y=2x-52 (D) y=12x+1

Short Answer

Step by step solution

– State the concept

– List the given data

– Write the equation

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Calculus

Geometry

Probability and Statistics

Theoretical and Mathematical Physics

Decision Maths

Pure Maths

Study anywhere. Anytime. Across all devices.

54. Choose the equation of the line through $(\frac{1}{2}, - \frac{3}{2})$ and $(- \frac{1}{2}, \frac{1}{2})$
$y = - 2 x - \frac{1}{2}$ (B) $y = - 3 x$ (C) $y = 2 x - \frac{5}{2}$ (D) $y = \frac{1}{2} x + 1$