Q12. What is an equation of the line ... [FREE SOLUTION]

Chapter 2: Q12. (page 78)

What is an equation of the line through $(2, - 4)$ and $(- 3, - 1)$ ?
(A). $y = - \frac{3}{5} x + \frac{26}{5}$ (B) $y = - \frac{3}{5} x - \frac{14}{5}$
(C) $y = \frac{3}{5} x - \frac{26}{5}$ (D) $y = \frac{3}{5} x + \frac{14}{5}$

Short Answer

Expert verified

The equation of the required straight line in slope-intercept form is $y = - \frac{3}{5} x - \frac{14}{5}$ . So, (B) 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 $(2, - 4)$ and $(- 3, - 1)$ .

Then, $(h, k) = (2, - 4)$ and $(a, b) = (- 3, - 1)$ .

– Write the equation

Put $(h, k) = (2, - 4)$ and $(a, b) = (- 3, - 1)$ in $\frac{y - k}{x - h} = \frac{b - k}{a - h}$ to get,

$\frac{y - (- 4)}{x - 2} = \frac{- 1 - (- 4)}{- 3 - 2}$

$\frac{y + 4}{x - 2} = \frac{- 1 + 4}{- 5}$ (Simplify)

$\frac{y + 4}{x - 2} = - \frac{3}{5}$ (Simplify)

$\frac{y + 4}{x - 2} (x - 2) = - \frac{3}{5} (x - 2)$ (Multiply both sides by (x-2)

$y + 4 = - \frac{3}{5} (x - 2)$ (Simplify)

$y + 4 = - \frac{3}{5} x + \frac{6}{5}$ (Distributive property)

$y + 4 - 4 = - \frac{3}{5} x + \frac{6}{5} - 4$ (Subtract 4 from both sides)

$y = - \frac{3}{5} x - \frac{14}{5}$ (Simplify)

So, the required equation of the straight line in slope-intercept form is $y = - \frac{3}{5} x - \frac{14}{5}$ .

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What is an equation of the line through $(2, - 4)$ and $(- 3, - 1)$ ?
(A). $y = - \frac{3}{5} x + \frac{26}{5}$ (B) $y = - \frac{3}{5} x - \frac{14}{5}$
(C) $y = \frac{3}{5} x - \frac{26}{5}$ (D) $y = \frac{3}{5} x + \frac{14}{5}$

Short Answer

Step by step solution

– State the concept

– List the given data

– Write the equation

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What is an equation of the line through 2,-4 and -3,-1? (A).y=-35x+265 (B) y=-35x-145 (C)y=35x-265 (D) y=35x+145

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

Mechanics Maths

Calculus

Logic and Functions

Applied Mathematics

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Study anywhere. Anytime. Across all devices.

What is an equation of the line through $(2, - 4)$ and $(- 3, - 1)$ ?
(A). $y = - \frac{3}{5} x + \frac{26}{5}$ (B) $y = - \frac{3}{5} x - \frac{14}{5}$
(C) $y = \frac{3}{5} x - \frac{26}{5}$ (D) $y = \frac{3}{5} x + \frac{14}{5}$