Answer:
The equation of the parallel line is x + 2y = a
Explanation:
* lets revise the general form of the linear equation
- The general form of the linear equation is ax + by + c = 0, where
a , b , c are real numbers
- The linear equation represented by a line its slope = -a/b and
intersects the y-axis at point (0 , -c/b) means y-intercept = -c/b
- The parallel lines have equal slopes and different y-intercepts
* Now lets solve the problem
- There is a line with equation x + 2y = 7
- Put the equation in the general form
∵ x + 2y = 7 ⇒ subtract 7 from both sides
∴ x + 2y - 7 = 0
∵ ax + by + c = 0 is the general form of the linear equation
∴ a = 1 , b = 2 , c = -7
∵ The slope of the line is -a/b
∴ The slope of the line -1/2
- We need to find the equation of the parallel line which has the
same slope
∵ The two lines are parallel
∴ Their slopes are equal
∴ The slope of the line is -1/2
∵ The slope depends on a and b
∴ The line has the same value of a and b
∵ a = 1 and b = 2
∵ ax + by + c = 0
∴ The equation of the line is x + 2y + c = 0
- To find c substitute x and y in the equation by the coordinates of
any point on the line
∵ The line passing through point (a , 0)
- Substitute x by a and y by 0
∴ a + 2(0) + c = =
∴ a + c = 0 ⇒ subtract a from both sides
∴ c = -a
- Substitute the value of c in the equation by - a
∴ The equation of the line is x + 2y - a = 0 ⇒ add a for both sides
∴ The equation of the line is x + 2y = a
* The equation of the parallel line is x + 2y = a
- They are equal in slopes and different in y-intercepts