I'm having a hard time with coming up with equations. Here's an example:
Complete the equation of the line through (−8,−2)and (−4,6)
Could anyone solve this and explain (as simple as possible) how you came up with the answer?
I'm sorry if this was a stupid question to ask but I'm having a really hard time with these types of things right now.
Thank you!
Well lets see!
Formula for a line is y = mx+b
(-8,-2) ==> x = -8 and its corresponding y is -2.
(-4, 6) ==> x = -4 and its corresponding y is 6.
Okay now, we must the slope formula, which is:
m = (y2 - y1) / (x2 - x1)
Using this formula you find your slope (which is your m).
Now put your value for m in the equation for the line (y = mx + b).
Now such choose one set of the points you provides and plug in its x value for the x in the equation, which already has your m (slope) in it (y = mx + b) and its corresponding y value. Now just solve for your b (y = mx+ b)
After that you are done! Congrats!
Solved:
So you take the coordinates and choose one set to be your (x1,y1) and the other one to be (x2,y2):
m = (6 - (-2)) / (-4-(-8)) = (8) / 4 = 2
Now plug in your m in this formula as shown:
y = mx + b = 2x+b
Now you must just choose either (-8,-2) or (-4,-6) as your x and corresponding y value and plug it in the formula above to find your b!
I will go for (-8,-2):
-2 = 2(-8) +b
-2 = -16 + b
-2 + 16 = b
14 = b
The final form would be y = 2x + 12
P.S. There is no such thing as a stupid question in math! Also good question and I commend your straightforwardness and your willingness to understand this concept better.
Side note: Use post one as preview for post 2!
slope = (6-(-2))/(-4-(-8) = 2
using the point (-4,6)
y-6 = 2(x+4)
y-6 = 2x + 8
y = 2x + 14
to check, sub both given points into this equation.
Both points work!
No problem at all! I'm here to help. Let's work through this together.
To find the equation of a line, we typically use the point-slope form or the slope-intercept form. In this case, I'll use the point-slope form. Here's how you can do it:
1. Identify the given points: (-8, -2) and (-4, 6). These are the coordinates of two points on the line.
2. Find the slope (m) of the line using the formula: m = (y2 - y1) / (x2 - x1), where (x1, y1) and (x2, y2) are the coordinates of the two points.
So, m = (6 - (-2)) / (-4 - (-8)).
= 8 / 4.
= 2.
3. Now that we have the slope (m), we can use the point-slope form of a line: y - y1 = m(x - x1).
Substitute one of the points and the value of the slope into the formula. Let's use (-8, -2):
y - (-2) = 2(x - (-8)).
Simplify: y + 2 = 2(x + 8).
4. Expand and simplify the equation:
y + 2 = 2x + 16.
Subtract 2 from both sides: y = 2x + 14.
So, the equation of the line passing through the points (-8, -2) and (-4, 6) is y = 2x + 14.
I hope this explanation helps you understand the process. If you have any more questions or need further clarification, feel free to ask!