A line with the slope of -2 contains the point (-3,0). Which point also lies on this line?
Answers:
a.) (-1,-4)
b.) (-1,4)
c.) (-2,1)
d.) (-2,-1)
y = -2x + b
0 = 6 + b
b = -6
so line is
y = -2x - 6
if x = -1, then y = -4, so a works
To find the point that lies on the line with a slope of -2 and passes through the point (-3, 0), we can use the point-slope form of a linear equation.
The point-slope form of a linear equation is given by y - y1 = m(x - x1), where (x1, y1) represents a point on the line, and m represents the slope of the line.
In this case, the point on the line is (-3, 0), and the slope is -2. Plugging these values into the point-slope form, we get:
y - 0 = -2(x - (-3))
Simplifying the equation, we have:
y = -2(x + 3)
Now, let's check which of the given points satisfy this equation.
For point (-1, -4):
-4 = -2(-1 + 3)
-4 = -2(2)
-4 = -4
For point (-1, 4):
4 = -2(-1 + 3)
4 = -2(2)
4 = -4
For point (-2, 1):
1 = -2(-2 + 3)
1 = -2(1)
1 = -2
For point (-2, -1):
-1 = -2(-2 + 3)
-1 = -2(1)
-1 = -2
Comparing the value of y for each point, we can conclude that none of the given points lie on the line with a slope of -2 and passing through the point (-3, 0).
To find another point that lies on a line with a given slope, you can use the point-slope form of the equation of a line.
The point-slope form of a line is given by:
y - y1 = m(x - x1)
Where (x1, y1) represents a point on the line, and m represents the slope of the line.
In this case, the slope is -2, and the given point is (-3,0).
Substituting the values into the point-slope form, we have:
y - 0 = -2(x - (-3))
Simplifying, we get:
y = -2(x + 3)
Now, to find which of the given points also satisfy this equation, you can substitute the x and y coordinates of each point into the equation and see which ones make the equation true.
Let's start with option (a) (-1,-4):
Plugging in x = -1 and y = -4 into the equation:
-4 = -2((-1) + 3)
-4 = -2(2)
-4 = -4
Option (a) (-1,-4) satisfies the equation, so it is another point that lies on the line.
Now let's check the other options:
Option (b) (-1,4):
Plugging in x = -1 and y = 4 into the equation:
4 = -2((-1) + 3)
4 = -2(2)
4 = -4
Option (b) (-1,4) does not satisfy the equation.
Option (c) (-2,1):
Plugging in x = -2 and y = 1 into the equation:
1 = -2((-2) + 3)
1 = -2(1)
1 = -2
Option (c) (-2,1) does not satisfy the equation.
Option (d) (-2,-1):
Plugging in x = -2 and y = -1 into the equation:
-1 = -2((-2) + 3)
-1 = -2(1)
-1 = -2
Option (d) (-2,-1) satisfies the equation, so it is another point that lies on the line.
Therefore, the points that also lie on the line with a slope of -2 are (-1,-4) and (-2,-1).
In conclusion, the correct answers are:
a.) (-1,-4)
d.) (-2,-1)