What is the standard form of the equation of the line passing through the point (-1,-2) and perpendicular to the line y= - 2/3x - 1?
a. 3x-2y=-1
b.3x-2y=1
c.3x+2y=1
d.3x+2y=-1
I don't understand, can anyone help me please?
Would this be B?
3(-1) - 2(-2) = 1
(-3) - (-4) =1
1 = 1
Yes.
However, I don't think you understand why. Just checking to see which of the lines contains your point is not enough.
The line y = -2/3x - 1 has slope -2/3.
Any line perpendicular to that line has slope -1/(-2/3) = 3/2.
So, now you have a slope and a point.
Using the point-slope form a line,
y-(-2) = 3/2 (x-(-1))
y+2 = 3/2 (x+1)
2(y+2) = 3(x+1)
2y + 4 = 3x + 3
3x - 2y = 1
Of course! I'd be happy to help you.
To find the standard form of the equation of a line perpendicular to another line, we'll need to follow a few steps:
Step 1: Find the slope of the given line
The given line has the equation y = -2/3x - 1. Comparing this equation to the standard form y = mx + b, we can see that the slope, m, is -2/3.
Step 2: Find the slope of the line perpendicular to the given line
For a line perpendicular to another line, the slopes are negative reciprocals. So, the slope of our perpendicular line would be the negative reciprocal of -2/3. To find the negative reciprocal, we flip the fraction and change the sign. In this case, the negative reciprocal of -2/3 is 3/2.
Step 3: Use the point-slope form to write the equation of the line
The point-slope form of a line is given by y - y1 = m(x - x1), where (x1, y1) represents a point on the line and m represents the slope.
We are given the point (-1,-2) that lies on the perpendicular line. Plugging in the values of the point and the slope into the point-slope form, we get:
y - (-2) = (3/2)(x - (-1))
Simplifying further, we have:
y + 2 = (3/2)(x + 1)
Step 4: Convert the equation to standard form
To convert the equation to standard form, we need to eliminate any fractions and rearrange the terms.
Multiplying through by 2 to eliminate the fraction, we have:
2(y + 2) = 3(x + 1)
2y + 4 = 3x + 3
Finally, we rearrange the equation to have the variables on the left side and the constant on the right side:
3x - 2y = -1
So, the standard form of the equation of the line passing through the point (-1,-2) and perpendicular to the line y = -2/3x - 1 is 3x - 2y = -1, which is option (d).