Question

Suppose a line passes through (a, -11) and (7,13), and is parallel to the line

y =2x + 8, What is the value of a? Write the equation of the line

Answer 1

see explanation

Explanation:

The equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

y = 2x + 8 ← is in slope- intercept form

with slope m = 2

Parallel lines have equal slopes

Calculate the slope between the 2 given points and equate to 2

Using the slope formula

m =
`(y_(2)-y_(1) )/(x_(2)-x_(1) )`

with (x₁, y₁ ) = (a, - 11) and (x₂, y₂ ) = (7, 13)

m =
`(13-(-11))/(7-a)` =
`(13+11)/(7-a)` =
`(24)/(7-a)` , then

`(24)/(7-a)` = 2 ( multiply both sides by 7 - a )

2(7 - a) = 24 ( divide both sides by 2 )

7 - a = 12 ( subtract 7 from both sides )

- a = 5 ( multiply both sides by - 1 )

a = - 5

--------------------------------------------------

y = 2x + c ← is the partial equation

To find c substitute (7, 13) into the partial equation

13 = 14 + c ⇒ c = 13 - 14 = - 1

y = 2x - 1 ← equation of parallel line

Answer 2

a=19

Explanation:

The slope of the equation is - 2 as it's parallel to the given line. Using two point slope form, (13-(-11))/(7-a)=-2. 24=-2(7-a), - 12=7-a, a=19