find the equation of the straight line that has slope m=4 and passes through the point(-1,-6)
Answers
Answer:
Well, if I have two points on a straight line, I can always find the slope; that's what the slope formula is for.
m = \dfrac{(4)-(2)}{(-2)-(1)} = \dfrac{2}{-3} = -\,\dfrac{2}{3}m=
(−2)−(1)
(4)−(2)
=
−3
2
=−
3
2
Now I have the slope and two points. I know I can find the equation (by solving first for "b") if I have a point and the slope; that's what I did in the previous example. Here, I have two points, which I used to find the slope. Now I need to pick one of the points (it doesn't matter which one), and use it to solve for b.
Using the point (–2, 4), I get:
y = mx + b
4 = (– 2/3)(–2) + b
4 = 4/3 + b
4 – 4/3 = b
12/3 – 4/3 = b
b = 8/3
...so y = ( – 2/3 ) x + 8/3.
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On the other hand, if I use the point (1, 2), I get:
y = mx + by=mx+b
2 = - \dfrac{2}{3} (1) + b2=−
3
2
(1)+b
2 = - \dfrac{2}{3} + b2=−
3
2
+b
\dfrac{6}{3} + \dfrac{2}{3} = b
3
6
+
3
2
=b
\dfrac{8}{3} = b
3
8
=b
So it doesn't matter which point I choose. Either way, the answer is the same:
\mathbf{\color{purple}{\mathit{y} = - \dfrac{2}{3}\mathit{x} + \dfrac{8}{3}}}y=−
3
2
x+
3
8
As you can see, once you have the slope, it doesn't matter which point you use in order to find the line equation. The answer will work out the same either way.