How do I write one equations in slope-intercept form, and three other lines in slope-intercept form that are perpendicular to the first line ??
for ex. If I pick the equation y=2/3x+4 for the first equation. and for the second line , the slope -2/3x +4 , how about the 3rd and 4th line?
do i choose any other value of b or slope?
Thank you!
the slope has to be the same, so just choose other values for b.
The problem is, a line with slope -2/3 is not perpendicular to a line with slope 2/3.
So the total of 4 equation have the same slope but different b values?
No, that was not the assignment. You pick any line.
Then determine slope of a perpendicular line, and pick three other lines with that slope, but with different b values.
Read things carefully.
Thank You
To write an equation in slope-intercept form, you need the equation to be in the form y = mx + b, where m represents the slope of the line and b represents the y-intercept.
For the first line, you have correctly written the equation as y = (2/3)x + 4, with a slope of 2/3 and a y-intercept of 4.
To find three other lines that are perpendicular to the first line, you will need to determine their slopes. Perpendicular lines have slopes that are negative reciprocals of each other. The negative reciprocal of 2/3 is -3/2.
For the second line, you can use the negative reciprocal slope of -3/2. So the equation would be y = (-3/2)x + b. You can choose any value for b to get a different line.
For the third line, use the same negative reciprocal slope of -3/2. Again, choose a different value for b.
For the fourth line, repeat the process by using the negative reciprocal slope of -3/2 and choose yet another value for b.
By picking different values for b, you will get three different lines that are perpendicular to the first line.
Remember, the slope-intercept form of an equation allows you to easily identify the slope and y-intercept of a line, which helps in graphing and understanding the behavior of the line.