MATH SOLVE

4 months ago

Q:
# The equation of the line passing through the ordered pair (a,0) and parallel to the line x + 2y = 7 is.

Accepted Solution

A:

Answer:The equation of the parallel line is x + 2y = aStep-by-step 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