using point slope form write the equation of the line through (1,-5) and perpindicular to -3x+2y=12

Question

please help asap bc i have no idea how to do this

Answer 1

Equation: -3x + 2y = 12 Point: (1, -5)

Point Slope form formula: y - y₁ = m(x - x₁)

For this problem, we need to find slope, x₁ and y₁ and x₂ and y₂.

To find the slope, we use the use the equation that is given to us. We have to change this equation into slope-intercept form, meaning it needs to look like this y = mx + b

To do this, you need to get y all by itself. So:

-3x + 2y = 12

+3x + 3x

______________

2y = 3x + 12 Divide all terms by 2 to get y by itself

y = 3/2x + 6

So our new equation is y= 3/2x + 6.

****Reminder: m is the slope and it is ALWAYS next to the x ONLY IF it is in the form above.

So, slope = 3/2. BUT our question is asking for a line that is PERPENDICULAR. So we need the slope that is PERPENDICULAR. To fin this slope, we take the slope we found and find the opposite reciprocal, meaning we do a flip and sign change. So it we flip 3/2, we get 2/3 and if we do a sign sign change, we go from positive to negative. Final slope will be -2/3.

Now we need to find x₁ and y₁ and x₂ and y₂. A point is given to us already. We are going to label this point (x₁ , y₂). So, x₁ = 1 and and y₁ = -5

Now that we have all this information, we plug and chug into our point slope formula and solve.

y - y₁ = m(x - x₁)

y - (-5) = -2/3(x - 1)

y + 5 = -2/3x + 2/3

- 5 - 5 Need to find a common denominator.

So -10/15 + 75/15 = 65/15 if we reduce 65/15 , we get 13/3

y = -2/3x - 7/2 + 13/3

So our final answer is y = -2/3x +13/3

Answer 2

Hello, Mia,

To put the equation in point slope form, move the terms around so that y is on the left and the rest are on the right. y = mx + b is a basic example. In this format, m is known as the "slope" of the line. It tells us how quickly the line rises, or falls. "b" is known as the "y intercept." It tells us where the line crosses the vertical axis (y) when x = 0.

Let's rewrite the equation you were given. Add "3x" to both sides and then divide both sides by "2." That will give us y =(3/2)x + 6. One can say the line "rises" as x becomes larger. The value of y increases by (3/2) every time x increase by "1." The line will cross the y axis at 6, when x is "0."

A perpendicular line intersects the first line at a 90 degree (right) angle. The way to make that happen is to change the slope so that it has the opposite slope. This is done by taking the negative inverse of the original slope. A line perpendicular to y = (3/2)x + 6 would have a slope of -(3/2) [the "negative inverse]. So the line y = -(3/2)x + 6 would be perpendicular to the first line. But we want the new line to intersect the point (1,5), which means the equation likely need a different value of b. To find which value of b that would make this equation work for (x,y) or (1.5), use these values in the new (perpendicular) line:

5 = -(3/2)*1 + b

b = 6.5

The equation meeting the requirements is thus y = -(3/2)X + 6.5

I hope this is clear. - Bob