Algebra 1 math homework

Question

Write the equation of the line perpendicular to

y=2/3x+1/3

that passes through the point

(−3,4).

Answer 1

Hello,

For lines to be perpendicular their slope has to have opposite signs and the slopes have to be the reciprocal of one another.

The given slope is 2/3x the perpendicular slope would be: -3/2x

There are two methods to solving: Method 1: Use the Slope Formula Y=MX+b

M = Slope of the Perpendicular line: -3/2x

use (-3,4) for (X,Y)

4 = -3/2(-3) + b - Plug in the X and Y and Simplify

9/2 + b

4 = 9/2 + b Now Solve for b

-9/2 -9/2

4/1 - 9/2 = -1/2

b= -1/2 Final Answer: y= -3/2x -1/2 this line is perpendicular to y=2/3x + 1/3

Method Two using Point Slope Formula

To write the equation use the Point Slope Formula: y-Y1=M(x-X1) Plug in (X1,Y1) using (-3,4)

Plug in M using the Perpendicular slope -3/2x

y-4 =-3/2(x- (-3) be careful watch the( minus and the -3) a negative times a negative creates a positive

y-4= -3/2(x+3) Now distribute

y-4 =-3/2x -9/2

+4 +4

-9/2 + 4/1 = -1/2

Final Answer y= -3/2x - 1/2 This line is perpendicular to y = 2/3x + 1/3 and passes through point (-3,4) when graphed.

Answer 2

The first step is to find the slope. To do this, we need to understand that perpendicular lines have opposite and reciprocal slopes to the current slope's line. This means, we want to find the opposite and reciprocal of 2/3. The opposite would be -2/3 and reciprocal of this would be -3/2.

Now that we have the slope of our perpendicular line, we can plug in the perpendicular slope into the slope intercept form and use the data point to solve for b.

So our new perpendicular line in slope intercept form is as follows: y=-3/2x +b. Now, we plug in the data point (-3,4) into the slope intercept form, 4=-3/2(-3)+b and solve for b. When we solve for b, we end up getting -1/2.

Our ultimate line we are looking for is y=-3/2x-1/2

Answer 3

Hello, Emily,

The given line, y=(2/3)x+1/3 , is in the form y = mx + b. "m" is the slope, (2/3) in this case. "b" is the y intercept, where the line crosses the y axis at x = 0.

The slope is key here. Parallel lines have the same slope. For example, the line y = (2/3)x -20 is parallel, but it crosses the y axis at -20 when x = 0. [y = (2/3)*(0) - 20, then y = -20 when x = 0].

But we are asked for a perpendicular line. Perpendicular lines have a slope equal to the negative inverse of the other line. In this case, that the slope of (2/3), invert it to (3/2) and add a minus to get a slope of -(3/2).

The equation thus takes the form y = -(3/2) + b

To find "b," enter the point given (-3,4), and solve for "b."

4 = -(3/2)*(-3) + b

4 = (9/2) + b

b = 4 - 4.5, or -0.5

The equation becomes y = -(3/2)x - 0.5

Bob

Answer 4

Emily,

For a line to be perpendicular to the given line, it's slope will be -1/m where m is 2/3 for this case. To have it pass through (-3,4)

y - y₀ = -1/m(x-x₀)

y - 4 = -3/2(x - (-3))

y = -3x/2 -9/2 +4

y = -3x/2 -1/2

Answer 5

Write the equation of the line perpendicular to

y=2/3x+1/3

that passes through the point

(−3,4).

Using equation of st line

y = mX +b

Comparing

m= 2/3 = Slope

Slope of perpendicular line = -1/m = -3/2

Line is y= -3/2 mX + C

Which passes through (-3, 4)

X= -3 and Y = 4

Plugging in

4 = -3/2 (-3) +C

Gives C = 4 - 9/2 = (8- 9) /2 = -1/2

Equation of line will be

y = -3/2 X -1/2 or

2Y = -3X-1