Consider the line 9x - 7y =4
What is the slope of a line parallel to this line?
What is the slope of a line perpendicular to this line?
9x - 7y =4
-7y = -9x + 4
y = 9x/7 - 4/7
Slope of line parallel: 9/7
Slope of line perpendicular: -7/9
Oh, lines and slopes, my favorite topic! Let's dive right in.
To find the slope of a line parallel to this one, we need to know that parallel lines have the same slope. So, we just need to rearrange the equation to get it in slope-intercept form, which is y = mx + b, where m is the slope.
9x - 7y = 4
First, let's move the 9x to the other side:
-7y = -9x + 4
Next, divide both sides by -7 to isolate y:
y = (9/7)x - 4/7
Hooray! We've got it in slope-intercept form! Now, we can see that the slope of this line is 9/7.
Now, for the perpendicular line... well, perpendicular lines have slopes that are negative reciprocals of each other. That means we need to find the negative reciprocal of 9/7.
To do that, we flip the fraction upside down and change its sign:
Negative reciprocal of 9/7 = -7/9
So, the slope of a line perpendicular to the given line is -7/9.
Hope that clarified things for you!
To find the slope of a line parallel or perpendicular to a given line, we need to examine the coefficients of x and y in the equation of the line.
Given the equation 9x - 7y = 4, we need to rewrite it into slope-intercept form y = mx + b, where m represents the slope.
Step 1: Rearrange the equation:
9x - 7y = 4
-7y = -9x + 4
7y = 9x - 4
Step 2: Divide every term by 7 to isolate y:
y = (9/7)x - (4/7)
From the equation y = (9/7)x - (4/7), we can see that the coefficient of x, which is 9/7, represents the slope of the line.
So, the answer is:
- The slope of a line parallel to this line is 9/7.
- The slope of a line perpendicular to this line is the negative reciprocal of 9/7, which is -7/9.
To determine the slope of a line parallel or perpendicular to the given line, we need to find the slope of the original line. The equation of the line, 9x - 7y = 4, can be rewritten in slope-intercept form (y = mx + b) by isolating the variable y.
Starting with the original equation:
9x - 7y = 4
Rearranging the equation, we get:
-7y = -9x + 4
Dividing both sides by -7, we get:
y = (9/7)x - 4/7
Now the equation is in slope-intercept form y = mx + b, where m represents the slope of the line. In this case, the coefficient of x, 9/7, represents the slope.
So, the slope of the given line is 9/7.
To find the slope of a line parallel to the given line, we need to remember that parallel lines have the same slope. Therefore, the slope of any line parallel to the given line is also 9/7.
To find the slope of a line perpendicular to the given line, we can use the fact that perpendicular lines have slopes that are negative reciprocals of each other. The negative reciprocal of 9/7 is -7/9.
Therefore, the slope of a line perpendicular to the given line is -7/9.