Answer:
Parallel:
Perpendicular:
Step-by-step explanation:
Hi there!
<u>What we must know:</u>
- Slope intercept form: where <em>m</em> is the slope and <em>b</em> is the y-intercept (the value of y when the line crosses the y-axis)
- Parallel lines always have the same slope
- Perpendicular lines always have slopes that are negative reciprocals (ex. 2 and -1/2, -6/7 and 7/6)
<u>Finding the Parallel Line</u>
Given this equation, we can identify that its slope (<em>m</em>) is . Because parallel lines always have the same slope, the slope of the line we're currently solving for would be as well. Plug this into :
Now, to find the y-intercept, plug in the given point (5,-2) and solve for <em>b</em>:
Therefore, the y-intercept is -3. Plug this back into :
Our final equation is .
<u>Finding the Perpendicular Line</u>
Again, the slope of this line is . The slopes of perpendicular lines are negative reciprocals, so the slope of the line we're solving for would be -5. Plug this into :
To find the y-intercept, plug in the point (5,-2) and solve for <em>b</em>:
Therefore, the y-intercept is 23. Plug this back into :
Our final equation is .
I hope this helps!