Consider the line 9x+4y=-9
What is the slope of a line parallel to this line?
What is the slope of a line perpendicular to this line?
For any equation in the form
Ax + By = C
the slope is -A/B
so the slope is ..... ?
The slopes of perpendicular lines are negative reciprocals of each other.
e.g. if the slope of some line is 4/11, then the slope of the perpendicular line is -11/4
let me know what you got.
To find the slope of a line parallel to the given line, we need to determine the slope of the given line. The given line is in the form of Ax + By + C = 0, where A and B are the coefficients of x and y, respectively.
In this case, the equation is 9x + 4y = -9, so the coefficient of x is 9 and the coefficient of y is 4.
To find the slope, we need to solve for y in terms of x. Let's rearrange the equation to isolate y:
4y = -9 - 9x
y = (-9 - 9x)/4
The slope of the given line is the coefficient of x, which is -9/4.
For a line to be parallel to the given line, it must have the same slope. Therefore, the slope of a line parallel to the given line is -9/4.
Now let's find the slope of a line perpendicular to the given line. The slope of a line perpendicular to another line is the negative reciprocal of the slope of the original line.
The negative reciprocal of -9/4 is 4/9.
Therefore, the slope of a line perpendicular to the given line is 4/9.
To find the slope of a line parallel or perpendicular to a given line, we need to know the slope-intercept form of the given line. The equation 9x + 4y = -9 is not in slope-intercept form, which is y = mx + b, where m is the slope and b is the y-intercept.
To find the slope of a line parallel to the given line, we need to remember that parallel lines have the same slope. To determine the slope of the given line, we can rearrange the equation to get it into the slope-intercept form.
9x + 4y = -9
Subtract 9x from both sides:
4y = -9 - 9x
Divide both sides by 4:
y = (-9 - 9x) / 4
Now we have the equation in the slope-intercept form y = mx + b, where m is the slope. By comparing this equation to y = mx + b, we can see that the slope (m) is -9/4.
Therefore, the slope of a line parallel to this line is also -9/4.
To find the slope of a line perpendicular to the given line, we need to remember that perpendicular lines have slopes that are negative reciprocals of each other. The negative reciprocal of -9/4 is 4/9.
Therefore, the slope of a line perpendicular to this line is 4/9.