Please let me know if I figured this out correctly.
Directions: Find the slope of a line perpendicular to the graph of each equation.
1) y= -x/5 - 7 Answer: Slope = 5
2) 2x + 3y=5 Answer: Slope = 3/2
Thank you!
[-1/(-1/5)] = 5 yes
[-1/(-2/3)] = 3/2 yes
Thank you!!!
You have correctly found the slopes of the lines perpendicular to the given equations. Here's an explanation on how to determine the slopes.
To find the slope of a line perpendicular to a given line, you can use the fact that the slopes of perpendicular lines are negative reciprocals of each other. So, to find the slope of a line perpendicular to a given equation, follow these steps:
1) Write the given equation in slope-intercept form, which is y = mx + b, where m is the slope and b is the y-intercept.
2) Once you have the equation in slope-intercept form, the slope of the given line is the coefficient of x. For example, in the equation y = -x/5 - 7, the slope is -1/5.
3) To find the slope of a line perpendicular to the given line, take the negative reciprocal of the original slope. In other words, flip the fraction and change its sign. So, the slope of the line perpendicular to -1/5 is 5.
Therefore, in your first example, the slope of a line perpendicular to y = -x/5 - 7 is indeed 5.
For the second example, you need to rearrange the equation 2x + 3y = 5 into slope-intercept form. First, isolate y by subtracting 2x from both sides, which gives you 3y = -2x + 5. Then, divide everything by 3 to get y = (-2/3)x + 5/3. Here, the slope of the given line is -2/3. Now, taking the negative reciprocal, the slope of the line perpendicular to -2/3 is 3/2.
So, you are correct in saying that the slope of a line perpendicular to 2x + 3y = 5 is 3/2. Well done!