Question

Heya! ~


`\underline{ \underline{ \tt{QUESTION}}} :`
- If the line y = mx + c passes through the point of intersection of the lines x - 2y = -1 and y = 2 and is perpendicular to the line y = 4x + 8 , then find the values of m and c.
Help!! Irrelevant / Random answers will be reported*

​

Answer 1

☆Answer :

• m = -¼
• c = 2¾

Answer in the picture.

Answer 2

`m = - (1)/(4)`

`c = 2 (3)/(4)`

Explanation:

Let's start by finding the point of intersection of the lines x -2y= -1 and y= 2.

x -2y= -1 -----(1)

y= 2 -----(2)

Substitute (2) into (1):

x -2(2)= -1

x -4= -1

x= 4 -1

x= 3

Thus, the point of intersection is (3, 2).

y= 4x +8

Slope= 4

The product of the slopes of perpendicular lines is -1.

4m= -1

m= -¼

y= -¼x +c

Since the line passes through (3, 2), we can substitute this coordinates into the equation to find the value of c.

When x= 3, y= 2,

`2 = - (1)/(4) (3) + c`

`c = 2 + (3)/(4)`

`c = 2 (3)/(4)`