Question

Use slopes and y-intercepts use slopes and y-intercepts to determine if the lines y=x/2 5 and x−2y=3. determine if the lines 3x−6y=−5 and 5x−3y=5 are parallel.

Answer 1

After rearranging the given equations into slope-intercept form, we find that the slopes of the two lines are 1/2 and 5/3, respectively. Because these slopes are not equal, the lines are not parallel.

Step-by-step explanation:

To determine if the lines 3x−6y=−5 and 5x−3y=5 are parallel, we need to find their slopes. According to slope-intercept form y = a + bx, where b represents the slope, we can rearrange these equations into this form to identify their slopes.

First, we solve 3x−6y=−5 for y:

1. 6y = 3x + 5
2. y = (3/6)x + 5/6
3. y = (1/2)x + 5/6

The slope for the first line is 1/2.

Next, we solve 5x−3y=5 for y:

1. 3y = 5x − 5
2. y = (5/3)x − 5/3

The slope for the second line is 5/3.

Since the slopes of the two lines, 1/2 and 5/3, are not equal, we can conclude that the lines are not parallel.