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

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

We can compare slopes and y-intercepts. The first equation has m=3/4 and b=7. The second has m=-2/5 and b=2. They are intersecting lines.

Explanation:

These equations are in the standard form of a line. We can convert to the slope-intercept by solving for y.

`3x-4y=28\\-4y=28-3x\\(-4y)/(-4) =(28-3x)/(-4) \\`

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

We can now convert the second equation.

`4x+10y=20\\10y=20-4x\\(10y)/(10)=(20-4x)/(10)`

`y=2-(4)/(10)x`

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

We can compare slopes and y-intercepts. The first equation has m=3/4 and b=7. The second has m=-2/5 and b=2. They are intersecting lines. This eliminates A and B. The answer based on the information given is likely D.