find the equation of the line perpendicular to the line 2x+3y=5 at the point (-2,3)
To find the equation of a line perpendicular to another line, we need to determine the slope of the given line and then use the negative reciprocal of that slope to find the slope of the perpendicular line.
Let's start by rearranging the equation 2x + 3y = 5 into slope-intercept form (y = mx + b), where m represents the slope and b represents the y-intercept.
2x + 3y = 5
3y = -2x + 5
y = (-2/3)x + 5/3
From this equation, we can see that the slope of the given line is -2/3.
The slope of a line perpendicular to this line will be the negative reciprocal of -2/3. The negative reciprocal is obtained by flipping the fraction and changing its sign.
So, the slope of the perpendicular line will be 3/2.
Now that we have the slope of the perpendicular line, we can use the point-slope form of a line to find its equation. The point-slope form is given by y - y1 = m(x - x1), where (x1, y1) is the given point (-2, 3) and m is the slope (3/2).
Using the point (-2, 3) and the slope 3/2, we can write the equation of the line:
y - 3 = (3/2)(x - (-2))
y - 3 = (3/2)(x + 2)
y - 3 = (3/2)x + 3
y = (3/2)x + 3 + 3
y = (3/2)x + 6
Therefore, the equation of the line perpendicular to 2x + 3y = 5 at the point (-2, 3) is y = (3/2)x + 6.
To find the equation of a line perpendicular to another line, we need to determine the slope of the original line and then find the negative reciprocal of that slope.
First, let's rearrange the equation 2x + 3y = 5 into slope-intercept form (y = mx + b), where m is the slope and b is the y-intercept.
2x + 3y = 5
3y = -2x + 5
y = (-2/3)x + 5/3
So, the slope of the original line is -2/3.
The negative reciprocal of -2/3 is 3/2. This is the slope of the line perpendicular to the original line.
Next, we have the point (-2, 3). Using the slope-intercept form, we can now find the equation of the perpendicular line.
y - y1 = m(x - x1)
y - 3 = (3/2)(x - (-2))
y - 3 = (3/2)(x + 2)
y - 3 = (3/2)x + 3
y = (3/2)x + 6
Therefore, the equation of the line perpendicular to 2x + 3y = 5 at the point (-2, 3) is y = (3/2)x + 6.
and your thinking is..?
perpendicular lines have opposite sign and reciprocal slopes from the original line you are given. put the first equation into proper form
y= (-2x/3)+(5/3)
the slope in this case is -2/3
Therefor a perpendicular line will have the slope 3/2.