What is B if the graph of the equation 3x=By+2 is perpendicular to the graph of 3y=-2x+4
the slopes must be negative reciprocals. The two lines have slopes of
3/B and -2/3
So, you know that you need to solve
(3/B)(-2/3) = -1
B = 2
B will unfortunately stand for "Beware of the Math Police!" because it looks like there's an equation showdown happening here! When two lines are perpendicular, their slopes are negative reciprocals of each other. So let's solve these equations to find the slopes and then have a little math magic!
Starting with 3x = By + 2, we can rewrite it as By = 3x - 2 and then divide everything by B to get y = (3/B)x - 2/B.
Looking at 3y = -2x + 4, we can write it as y = (-2/3)x + 4/3.
Comparing the slopes, we have (3/B) and (-2/3). To be perpendicular, these slopes need to be negative reciprocals. So, solving (3/B) * (-2/3) = -1, we get B = 2.
So, B is the mysterious number that makes the graphs perpendicular, but don't forget to keep an eye out for those Math Police! They're always ready to crack down on those pesky math equations!
To find the value of B, we need to find the slope of the given equation 3x=By+2 and the slope of the equation 3y=-2x+4.
First, let's rearrange the given equation 3x=By+2 in slope-intercept form (y = mx + b), where m is the slope:
3x = By + 2
By = 3x - 2
y = (3/B)x - 2/B
By comparing this equation to the slope-intercept form y = mx + b, we can see that the slope (m) of the equation is 3/B.
Now, let's rearrange the equation 3y = -2x + 4 in slope-intercept form:
3y = -2x + 4
y = -(2/3)x + 4/3
By comparing this equation to the slope-intercept form y = mx + b, we can see that the slope (m) of this equation is -2/3.
Since we want the graphs of the equations to be perpendicular, the product of their slopes should be -1. So, we have:
(3/B) * (-2/3) = -1
Simplifying this equation, we get:
-6/(3B) = -1
Cross-multiplying, we have:
-6 = -1 * (3B)
-6 = -3B
Dividing by -3, we get:
B = 2
Therefore, if the graph of the equation 3x=By+2 is perpendicular to the graph of 3y=-2x+4, B must be equal to 2.
To find the value of B in the equation 3x = By + 2, given that the graph is perpendicular to the graph of 3y = -2x + 4, we need to use the concept of slope.
First, let's rearrange the equation 3y = -2x + 4 to the slope-intercept form, y = mx + b, where m represents the slope. So we have:
3y = -2x + 4
Divide both sides by 3:
y = (-2/3)x + (4/3)
Comparing this equation to the equation 3x = By + 2, we can see that the slope of the second equation is B/3 (since B is multiplied by y).
For two lines to be perpendicular, their slopes must be negative reciprocals of each other. So, let's find the negative reciprocal of (-2/3).
To find the negative reciprocal of a fraction, we need to flip it and change the sign.
So, the negative reciprocal of (-2/3) is (3/2) with the opposite sign.
Therefore, B/3 = 3/2.
To find the value of B, we can cross multiply and solve for B:
2B = 3 * 3
2B = 9
B = 9/2
B = 4.5
So, B is equal to 4.5.