Help me with this problem. Write an equation of line containing the given point and perpendicular to the give line (4-2); 9x+2y=3
help me with this.
We need to find the slope of the original line
One way is to put it in the form y = m x + b
2 y = -9 x + 3
y = -9/2 x + 3/2
so the slope m = -9/2
now the slope of the perpendicular m' = -1/m
= 2/9
so our line has the form
y = -2 x/9 + b
now put 4 in for x and -2 in for y and find b
easy way:
A line perpendicular to 9x + 2y = 3 must be
2x - 9y = k
sub in your given point to find k,
all done!
To find an equation of a line that is perpendicular to the given line and passes through the given point (4, -2), we need to follow a few steps:
Step 1: Find the slope of the given line.
Step 2: Determine the slope for the line perpendicular to the given line by using the negative reciprocal of the slope found in Step 1.
Step 3: Use the point-slope form of the equation to write the equation of the line.
Let's go through each step in detail:
Step 1: Find the slope of the given line.
The given line equation is 9x + 2y = 3. To find the slope, we need to rearrange the equation into slope-intercept form (y = mx + b), where m is the slope.
First, isolate the term with 'y':
2y = -9x + 3
Divide both sides of the equation by 2 to solve for 'y':
y = -(9/2)x + 3/2
From the equation, we can see that the slope (m) is -(9/2).
Step 2: Determine the slope for the line perpendicular to the given line.
The slope of a line perpendicular to another line is the negative reciprocal of the slope of that line.
Therefore, the slope for the line perpendicular to -(9/2) is the negative reciprocal of -(9/2), which is 2/9.
Step 3: Use the point-slope form to write the equation of the line.
The point-slope form of an equation is y - y1 = m(x - x1), where (x1, y1) is the given point.
Substituting the values into the point-slope form, we get:
y - (-2) = (2/9)(x - 4)
Simplifying and rearranging the equation:
y + 2 = (2/9)x - 8/9
y = (2/9)x - 26/9
Therefore, the equation of the line containing the given point (4, -2) and perpendicular to the line 9x + 2y = 3 is y = (2/9)x - 26/9.