Question

find the equation of a straight line which passes through the points (0,4) and (5,3)

Answer 1

Answer:

Let the line cut the x axis at (a,0) and y−axis at (0,b).

Therefore

It is given that the point (−4,3) divides the line internally in 5:3 ratio. Hence applying the formula for internal division of line segment, we get

83a=−4 and 85b=3

Hence a=3−32 and b=524

Using slope intercept form we get

3−32x+524y=1

9x−20y+96=0

Step-by-step explanation:

Correct option is

A

9x−20y+96=0

Answer 2

Given :-

A straight line passes through the two points (0, 4) and (5, 3)

To find :-

Equation of straight line

Solution :-

Inorder to find the required equation of straight line, we will use two point form in which we obtain the equation of straight line whose two coordinates are given through which the line passes.

Two-point form of straight line:

$\boxed{\sf y-y_1 = \dfrac{y_2-y_1}{x_2-x_1}(x-x_1)}$

Here,

• (x1, y1) = (0, 4)
• (x2, y2) = (5, 3)
• (x, y) are variables

So, on substituting these values in the equation of two point form, we get:

$\sf \implies y-y_1 = \dfrac{y_2-y_1}{x_2-x_1}(x-x_1)$

$\sf \implies y - 4 = \dfrac{3 - 4}{5 - 0}(x-4)$

$\sf \implies y - 4 = - \dfrac{1}{5}(x-4)$

$\sf \implies - 5(y - 4) = (x-4)$

$\sf \implies - 5y + 20= x-4$

$\sf \implies 20 + 4= x + 5y$

$\sf \implies 24= x + 5y$

Hence this is the required equation of straight line.

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Straight lines lesson all formulas

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