a line passes through the point (-3,2)and has a slope of 1/3.which of the following points also lies on this line?
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y=1/3x+3
The equation of the line that passes through the point (-3,2) and has a slope of 1/3 is:
y = 1/3 x + 3
To check if a point lies on this line, we simply substitute the x and y values of the point into the equation and see if it is a true statement.
For example, let's check if the point (0,3) lies on this line:
y = 1/3 x + 3
3 = 1/3(0) + 3
3 = 3
Since this is a true statement, the point (0,3) lies on the line.
Well, well, well, let me put on my mathematician's clown nose for this one!
To figure out which point lies on the line with a slope of 1/3 passing through (-3, 2), we can use the good old slope-intercept formula: y = mx + b.
Here, m represents the slope. So we have y = (1/3)x + b.
Now, we can plug in the coordinates (-3, 2) and solve for b.
2 = (1/3)(-3) + b
2 = -1 + b
We find that b must be 3 for this line.
Now let's test the other points to see which one fits our equation.
a) (-1, 0)
Plugging in the coordinates, we have:
0 = (1/3)(-1) + 3
0 = -1/3 + 3
Oops, it looks like the world of math disagrees! (-1, 0) does not lie on the line with the slope of 1/3 passing through (-3, 2).
So, none of the given points lie on the line! Maybe this is a line that's just passing through its own imagination—pretty imaginative, if you ask me!
To find which point lies on the line passing through (-3, 2) with a slope of 1/3, we can substitute the coordinates of each point into the equation of the line.
The equation of a line in point-slope form is given by:
(y - y1) = m(x - x1)
where (x1, y1) are the coordinates of a point on the line, and m is the slope of the line.
Substituting the values (-3, 2) and m = 1/3 into the equation, we get:
(y - 2) = (1/3)(x - (-3))
Simplifying the equation, we have:
(y - 2) = (1/3)(x + 3)
Now, we can substitute the coordinates of each given point into the equation and check which one satisfies the equation.
Let's check the points one by one:
1. Point A: (4, 3)
- Substituting (x, y) = (4, 3) into the equation:
(3 - 2) = (1/3)(4 + 3)
1 = (1/3)(7)
1 = 7/3
Since the equation is not satisfied, point A does not lie on the line.
2. Point B: (-3, 1)
- Substituting (x, y) = (-3, 1) into the equation:
(1 - 2) = (1/3)(-3 + 3)
-1 = 0
Again, the equation is not satisfied, so point B does not lie on the line.
3. Point C: (0, 1)
- Substituting (x, y) = (0, 1) into the equation:
(1 - 2) = (1/3)(0 + 3)
-1 = 1
Once more, the equation is not satisfied, so point C does not lie on the line.
4. Point D: (-6, 0)
- Substituting (x, y) = (-6, 0) into the equation:
(0 - 2) = (1/3)(-6 + 3)
-2 = -1
The equation is satisfied this time, so point D, (-6, 0), lies on the line passing through (-3, 2) with a slope of 1/3.
Therefore, the correct answer is Point D: (-6, 0).
Point-slope equation of a straight line:
y − y1 = m ( x − x1 )
In this case:
x1 = - 3 , y1 = 2
y − 2 = 1/3 [ x − ( - 3) ]
y − 2 = 1/3 ( x + 3 )
y − 2 = 1/3 x + 1
Add 2 to both sides
y = 1/3 x + 3