SOLUTION: Tell whether the two given equations are perpendicular, parallel, the same, or none of these. y= -1/2x+3 8x+16y=32

Question 181846: Tell whether the two given equations are perpendicular, parallel, the same, or none of these.
y= -1/2x+3
8x+16y=32
Found 2 solutions by vleith, solver91311:
Answer by vleith(2983) (Show Source): You can put this solution on YOUR website!
Find the slopes of each line

so m=-1/2

so m = -1/2 on this line
Both lines have the same slope ... so they are parallel lines
They have different y intercepts, so they are different lines.
Answer by solver91311(24713) (Show Source): You can put this solution on YOUR website!

Your first equation is in slope-intercept form:

where m is the slope and b is the y-intercept meaning the point (0,b) where the line intersects the y-axis.

You need to arrange your second equation into the same form, so that you can see the slope and y-intercept of the second equation.

Use the following rules:

If the slopes AND y-intercepts of the two equations are the same, they are equations of the same line.

If the slopes are equal but the y-intercepts are different, they are equations of two different parallel lines.

If the slopes are negative reciprocals of one another, then the lines are perpendicular.

If none of the above relationships hold, then they are not the same, not parallel, and not perpendicular.

John

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