Question

Find the equation of the line passing through the point (2,3) and perpendicular to the straight line 2x+4y=7​

Answer 1

Answer:

Equation of the line = 2x - y - 1 = 0

Step-by-step explanation:

Given:

• The line passes through the point (2, 3)
• It is perpendicular to the line 2x + 4y = 7

To Find:

• The equation of the straight line

Solution:

Given that the line is perpendicular to the line 2x + 4y = 7.

This can be written in the form y = mx + c,

4y = 7 - 2x

y = 7/4 - 1/2 x

where m = -1/2 = slope of the line.

Let the slope of the given line be m₁ and the other line be m₂

Since the lines are perpendicular,

m₁ m₂ = -1

-1/2 × m₂ = -1

m₂ = 2

Hence slope of the second line is 2.

Therefore the equation of the line can be written as,

y = m₂ x + c

y = 2x + c

But given that the line passes through the point (2, 3)

Therefore,

3 = 2 × 2 + c

3 = 4 + c

c = -1

Substitute the value of c.

y = 2x - 1

2x - y - 1 = 0

Therefore the equation of the line is 2x - y - 1 = 0

Answer 2

Equation of the line = 2x-y-1 = 0

Given

●The line passing through the Point(2,3)

○It is perpendicular to the Line 2x+4y= 7

To Find

• The equation of straight line

Solution

Given that the Line is perpendicular to the line 2x+4y = 7

We can Write In this form y = mx+c

4y = 7-2x

Y=7÷4 - 1 ÷ 2x

Where M = - 1÷2 Slope of the line

Let the slope of the given line be m1 and m2

▪︎Lines are perpendicular

m1 m2 = -1

-1/2×m2 = -1

m2 = 2

■ solpe of 2nd line is 2

The equation of line can be Written as

y = m2 x + c

y = 2x + c

But the line passes through the point (2,3)

Therefore

3 = 2×2+c

3 = 4+c

c = -1

Now let us Substitute The value of c

Y = 2x-1

2x - y - 1 = 0

Therefore The equation of line is 2x - y - 1 = 0