Question

The slopes are different, and the y-intercepts are different. The slopes are different, and the y-intercepts are the same. The slopes are the same, and the y-intercepts are different. The slopes are the same, and the y-intercepts are the same.

Answer 1

The slopes are the same and the y-intercepts are different.

Step-by-step explanation:

Given:

`\begin{gathered} x+2y=8 \\ 2x+4y=12 \end{gathered}`

Recall that the slope-intercept equation of a line is generally given as;

`y=mx+b`

where;

m = slope of the line

b = y-intercept of the line

Let's go ahead and rewrite the first equation in slope-intercept form as seen below;

`\begin{gathered} x+2y=8 \\ 2y=-x+8 \\ y=-(1)/(2)x+(8)/(2) \\ y=-(1)/(2)x+4 \end{gathered}`

We can see from the above that the slope(m) of the first equation is -1/2 and the y-intercept(b) is 4.

Let's go ahead and rewrite the second equation in slope-intercept form as seen below;

`\begin{gathered} 2x+4y=12 \\ 4y=-2x+12 \\ y=-(2)/(4)x+(12)/(4) \\ y=-(1)/(2)x+3 \end{gathered}`

We can see from the above that the slope(m) of the second equation is -1/2 and the y-intercept(b) is 3.

We can see from the above that, for the two equations, the slopes are the same, and the y-intercepts are different.