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

Answer:

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

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;

$\begin{gathered} x+2y=8 \\ 2y=-x+8 \\ y=-\frac{1}{2}x+\frac{8}{2} \\ y=-\frac{1}{2}x+4 \end{gathered}$

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;

$\begin{gathered} 2x+4y=12 \\ 4y=-2x+12 \\ y=-\frac{2}{4}x+\frac{12}{4} \\ y=-\frac{1}{2}x+3 \end{gathered}$

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.