Question

Please answer the question in the attached picture!​

Answer 1

y = -
`(7)/(2)` x + 20

Explanation:

The first step is to find the point of intersection of the 2 given lines.

x + y = 10 → (1)

3x - 4y + 12 = 0 ( subtract 12 from both sides )

3x + 4y = - 12 → (2)

multiplying (1) by 4 and adding the result to (2) will eliminate y

4x + 4y = 40 → (3)

add (2) and (3) term by term to eliminate y

(3x + 4x) + (- 4y + 4y) = - 12 + 40

7x + 0 = 28

7x = 28 ( divide both sides by 7 )

x = 4

substitute x = 4 into either of the 2 original equations and solve for x

substituting into (1)

4 + y = 10 ( subtract 4 from both sides )

y = 6

point of intersection is (4, 6 )

The equation of a line in slope- intercept form is

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

y = -
`(7)/(2)` x +9 ← is in slope- intercept form

with slope m = -
`(7)/(2)`

• Parallel lines have equal slopes , then

y = -
`(7)/(2)` x + c ← is the partial equation

to find c, substitute (4, 6 ) for x and y into the partial equation

6 = -
`(7)/(2)` (4) + c = - 14 + c ( add 14 to both sides )

20 = c

y = -
`(7)/(2)` x + 20 ← equation of parallel line