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

Answer:

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.

Step-by-step explanation:

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

$3x-4y=28\\-4y=28-3x\\\frac{-4y}{-4} =\frac{28-3x}{-4}$

$y=-7+ \frac{3}{4} x$

We can now convert the second equation.

$4x+10y=20\\10y=20-4x\\\frac{10y}{10}=\frac{20-4x}{10}$

$y=2-\frac{4}{10}x$

$y=2-\frac{2}{5}x$

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.