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Home » Find the equation of a line that has y – intercept – 4 and is parallel to the line joining (2, –5) and (1, 2).
Find the equation of a line that has y – intercept – 4 and is parallel to the line joining (2, –5) and (1, 2).
CBSE | Class 11 | Exercise 23.3 | Maths | RD Sharma | Straight Lines
Find the equation of a line that has y – intercept – 4 and is parallel to the line joining (2, –5) and (1, 2).

Given:

A line segment joining

    \[\left( 2,\text{ }-\text{ }5 \right)\text{ }and\text{ }\left( 1,\text{ }2 \right)\]

if it cuts off an intercept

    \[-\text{ }4\]

from y–axis

By using the formula,

The equation of line is

    \[y\text{ }=\text{ }mx\text{ }+\text{ }C\]

It is given that,

    \[c\text{ }=\text{ }-\text{ }4\]

Slope of line joining

    \[({{x}_{1}}-\text{ }{{x}_{2}})\text{ }and\text{ }({{y}_{1}}-\text{ }{{y}_{2}})\]

RD Sharma Solutions for Class 11 Maths Chapter 23 – The Straight Lines - image 8

So, Slope of line joining

    \[\left( 2,\text{ }-\text{ }5 \right)\text{ }and\text{ }\left( 1,\text{ }2 \right),\]

RD Sharma Solutions for Class 11 Maths Chapter 23 – The Straight Lines - image 9

    \[m\text{ }=\text{ }-\text{ }7\]

The equation of line is

    \[y\text{ }=\text{ }mx\text{ }+\text{ }c\]

Now, substitute the values, we get

    \[y\text{ }=-\text{ }7x\text{ }-\text{ }4\]

    \[y\text{ }+\text{ }7x\text{ }+\text{ }4\text{ }=\text{ }0\]

∴ The equation of line is 

    \[y\text{ }+\text{ }7x\text{ }+\text{ }4\text{ }=\text{ }0\]

i

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