Tell whether the lines for then pair of equations are parallel, perpendicular, or neither?

y=-2/3x +1

2x-3y=-3

Lucina's conclusion is correct, but based on an incorrect result.

The slope of the first line is -2/3
the slope of the 2nd line is 2/3

so they are neither parallel nor parallel

Lucina stated that their slopes were equal, if they had been equal, then the lines would have been parallel.

Thank you for the help. I needed it on a worksheet problem and I was stuck on this for hours. Thank you!

thank you

Your welcome :)

Well, if we rearrange the second equation to solve for y, we get y = (2/3)x + 1. So the slopes of both equations are -2/3 and 2/3, respectively. Since the product of these slopes is -1, the lines are perpendicular! They must really enjoy being at right angles with each other.

Converting 2x-3y=-3 into slope intercept form gives us:

y= -2/3x+1

This means that these two lines are the same, so this means they are neither parallel or perpendicular

To determine whether the lines formed by the pair of equations are parallel, perpendicular, or neither, we need to compare the slopes of the two lines.

The given equations are:
1) y = (-2/3)x + 1
2) 2x - 3y = -3

To find the slope of the first equation, we can compare it with the standard form of a linear equation, y = mx + b, where "m" represents the slope.
From the given equation, y = (-2/3)x + 1, we can observe that the coefficient of "x" (-2/3) is the slope of the line.

So, the slope of the first equation is -2/3.

To determine the slope of the second equation, we need to rewrite it in slope-intercept form, y = mx + b.
Start by rearranging the equation:
2x - 3y = -3
-3y = -2x - 3
y = (2/3)x + 1

From the rearranged equation, we can see that the slope of the second equation is 2/3.

Now that we have the slopes of both lines, we can compare them:
Slope of the first equation = -2/3
Slope of the second equation = 2/3

If the slopes of two lines are equal, the lines are parallel.
If the slopes of two lines are negative reciprocals (opposite signs and inverted), the lines are perpendicular.
If the slopes are neither equal nor negative reciprocals, the lines are neither parallel nor perpendicular.

In this case, the slopes -2/3 and 2/3 are negative reciprocals of each other. Therefore, the lines formed by these equations are perpendicular.