Are these two equations perpendicular when graphed?
y=9x-2 and 3y=7-x
correct, one has a slope of 9, the other a slope of -1/3
9 * -1/3 ≠ -1
Mmmmhhh?
Do you know how to read off the slope if the equation is in the form
y = mx + b ?? (one is already in that form)
Is one slope the negative reciprocal of the other ??
I think that both are not perpendicular to each other when graphed.
To determine if two equations are perpendicular when graphed, we need to compare their slopes.
First, let's rewrite both equations in slope-intercept form, which is in the form y = mx + b, where m represents the slope:
1. Equation 1: y = 9x - 2
In this equation, the slope (m) is 9.
2. Equation 2: 3y = 7 - x
Re-arrange this equation to get it in the slope-intercept form:
3y = -x + 7 (by subtracting x from both sides)
Divide both sides by 3:
y = (-1/3)x + 7/3
In this equation, the slope (m) is -1/3.
Now that we have the slopes, we can determine if they are perpendicular. Two lines are perpendicular when the product of their slopes is -1. In other words, if the slopes of the lines are negative reciprocals of each other, they are perpendicular.
Let's calculate the product of the slopes:
Product of the slopes: (9) * (-1/3) = -3
Since the product of the slopes is -3 (not -1), the two lines are not perpendicular when graphed.