math how to solve?

Question

hi i need help to solve problems like this can you please help

Determine the equations of the following lines perpendicular to

Y=3x-4 with the same x-intercept as 3x-2y-6=0

can you please help me to get the answer, i don't just want the answer but how i can solve other questions like this.

Answer 1

Perpendicular lines have a negative inverse slope to the lines they are perpendicular too.

eg.
m ┴ -1/m

So given the equation,

Y = 3x - 4

the slope is 3, therefore the negative inverse is -1/3. That is the slope you need to help you create your equation. The next part states that the equation must have the same x-intercept as the equation,

3x-2y-6 = 0

The x-intercept is where the line crosses the X-axis. What is the value of Y at the X-axis? It's equal to 0. So how do we find the X component? We substitute Y with 0 and solve for X.

3x - 2(0) - 6 = 0
3x - 6 = 0
3x = 6
x = 2

So now we know a point in the equation is (2,0). Now we have all we need to create a standard equation of the form

y = mx + b

y - 0 = -1/3(x - 2)
y = -1/3(x - 2)

y = (-1/3)x + 2/3

Answer 2

perpendicular means that the cooeficient is the negative reciprocal of the current coefficient, so the perpendicular equation to the first equation is y=-1/3x-4. you have to solve the other equation for x by adding 6 to both sides and adding 2y to both sides then dividing both sides by 3. then plug in 0 for y to find the x intercept.

Answer 3

find x int of the 2nd equation.

3x-2y-6=0
3x=2y+6
x=2/3y+2
x int=2

Then you find the equation to the line perpendicular to the 1st equation. This is the opposite of the reciprocal.
So it would be -1/3.

The final equation would be: -3y+2=x
OR it would be: y=-1/3x+2/3

Answer 4

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