Q53. Find an equation of the line thr... [FREE SOLUTION]

Chapter 2: Q53. (page 80)

Find an equation of the line through $(0, - 3)$ and $(4, 1)$
A. $y = - x + 3$ (B) $y = - x - 3$ (C) $y = x - 3$ (D) $y = x + 3$

Short Answer

Expert verified

The equation of the required straight line is $y = x - 3$ . So, (C) 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 $(0, - 3)$ and $(4, 1)$ .

Then, $(h, k) = (0, - 3)$ and $(a, b) = (4, 1)$ .

– Write the equation

Put $(h, k) = (0, - 3)$ and $(a, b) = (4, 1)$ in $\frac{y - k}{x - h} = \frac{b - k}{a - h}$ to get,

$\frac{y - (- 3)}{x - 0} = \frac{1 - (- 3)}{4 - 0}$

$\frac{y + 3}{x} = \frac{1 + 3}{4}$ (Simplify)

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

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

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

$y + 3 = x$ (Simplify)

$y + 3 - 3 = x - 3$ (Subtract 3 from both sides)

$y = x - 3$ (Simplify)

So, the required equation of the straight line is $y = x - 3$ .

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Column A	Column B
The x-coordinate of point Q	The y-coordinate of point P

91影视

Find an equation of the line through $(0, - 3)$ and $(4, 1)$
A. $y = - x + 3$ (B) $y = - x - 3$ (C) $y = x - 3$ (D) $y = x + 3$

Short Answer

Step by step solution

– State the concept

– List the given data

– Write the equation

One App. One Place for Learning.

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91影视

Find an equation of the line through 0,-3 and 4,1A. y=-x+3 (B) y=-x-3 (C) y=x-3 (D) y=x+3

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

Geometry

Calculus

Logic and Functions

Theoretical and Mathematical Physics

Applied Mathematics

Statistics

Study anywhere. Anytime. Across all devices.

Find an equation of the line through $(0, - 3)$ and $(4, 1)$
A. $y = - x + 3$ (B) $y = - x - 3$ (C) $y = x - 3$ (D) $y = x + 3$