Question

What is the slope-intercept form for each equation in this system? Compare the slopes and y-intercepts to describe the graph of the system. 3x - 4y = 28 4x + 10y = 20 A) y = 3 4 x − 7; y = −2 5 x + 2; one line B) y = - 3 4 x − 7; y = −2 5 x + 2; parallel lines Eliminate C) y = 3 4 x − 7; y = 2 5 x + 2; intersecting lines D) y = 3 4 x − 7; y = −2 5 x + 2; intersecting lines

Answer 1

3x - 4y = 28
4x + 10y = 20
First we rewrite the system of equations:
Equation 1:
3x - 4y = 28
3x - 28 = 4y
(3/4) x - 7 = y
Equation 2:
4x + 10y = 20
10y = 20 - 4x
y = 2 - (2/5) x
We have then:
y = (3/4) x - 7
y = - (2/5) x + 2
One line has a positive slope and the other line has a negative slope.
Thus, both lines are connected.

Answer:
D) y = 3/4 x - 7; y = -2/5 x + 2; intersecting lines

Answer 2

The slope - intercept form of the equations are :
`y = (3)/(4) x - 7` and
`y = - (2)/(5) x + 2`

Given the standard form of the equations :

• 3x - 4y = 28 - - - - (1)

• 4x + 10y = 20 - - - - - (2)

The General form of a slope - intercept equation :

• y = bx + c

For equation (1) :

3x - 4y = 28

Make y the subject

-4y = 28 - 3x

Divide both sides by - 4 to isolate y

y = -7 + 3/4x

`y = (3)/(4) x - 7`

For equation (2) :

4x + 10y = 20

Make y the subject

10y = 20 - 4x

Divide through by 10 to isolate y

y = 2 - 2/5x

`y =- (2)/(5) x + 2`

Hence, the slope - intercept equations are :
`y = (3)/(4) x - 7` and
`y = - (2)/(5) x + 2`

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