1) Use the point on the line and the slope m of the line to find three additional points through which the line passes. (There are many correct answers.)
(1, 6), m is undefined
the options for 2 are
a) (1, -2), (-1, -2), (-2, -2)
b) (1, -6), (3, -6), (5, -6)
c) (1, 1), (1, 2), (1, 0)
d) (2, 6), (5, 6), (0, 6)
e) (-1, 6), (-1, 5), (-1, 4)
2) Use the point on the line and the slope m of the line to find three additional points through which the line passes. (There are many correct answers.)
(0, −9), m = −2
a) (1, -2), (-2, 4), (2, -4)
b) (3, -15), (1, -11), (-1, -7)
c) (-2, 13), (-3, 15), (2, 5)
d) (1, -7), (2, -9), (4, -13)
e) (1, -10), (5, -14), (4, -13)
In #1, since the slope is undefined, the line must be a vertical line.
If a line is vertical all its x values must be the same.
Looking at the given point (1,6) , mmmhhhh?
#2, clearly the equation is y = -2x - 9
Which set of points satisfies this equation?
(btw, if the first point in a set fails, there is no need to try the other two)
for question 2, the answer would be b
yes
To find three additional points through which a line passes, given a point on the line and the slope of the line, you can use the point-slope form of a linear equation. The point-slope form is:
y - y1 = m(x - x1)
where (x1, y1) is the given point on the line and m is the slope.
Let's solve each problem step by step:
1) Given point: (1, 6), m is undefined.
Since the slope is undefined, it means that the line is vertical and has the form x = a, where "a" is a constant. In this case, x = 1. This means that the line passes through infinitely many points, with x-coordinate equal to 1.
The correct answer is option c) (1, 1), (1, 2), (1, 0).
Explanation:
- Plug in x = 1 into the equation x = 1, and you get three points: (1, 1), (1, 2), (1, 0).
- All three points have x-coordinate equal to 1, satisfying the equation of a vertical line x = 1.
2) Given point: (0, -9), m = -2.
Using the point-slope form, we can find three additional points on the line.
We will use the formula: y - y1 = m(x - x1)
Plug in values: (x1, y1) = (0, -9), m = -2.
The equation becomes: y - (-9) = -2(x - 0)
Simplify: y + 9 = -2x
Now, you can choose any x-value and solve for the corresponding y-value to get three additional points.
The correct answer is option d) (1, -7), (2, -9), (4, -13).
Explanation:
- Pick three different x-values, such as x = 1, 2, 4.
- Substitute these values into the equation y + 9 = -2x and solve for y.
- For x = 1, we get y + 9 = -2(1), which gives y + 9 = -2 and y = -11. The point is (1, -11).
- For x = 2, we get y + 9 = -2(2), which gives y + 9 = -4 and y = -13. The point is (2, -13).
- For x = 4, we get y + 9 = -2(4), which gives y + 9 = -8 and y = -17. The point is (4, -17).
These three points, together with the given point (0, -9), satisfy the equation of the line y + 9 = -2x. Thus, they are valid additional points through which the line passes.