(0,-5), m=3/2
a) find the equation of the line
b) find three other points that go through the line
a. y=3/2x-5
To avoid ambiguity, I would put it as:
a. y = (3/2)x - 5
b. Write the line as
y=f(x)=(3/2)x - 5
Then f(0) = (3/2)*0 - 5 = -5
(0,-5) is on the line.
Since f(-1)=-13/2 and f(1) = -7/2
we conclude that (-1,-13/2) and (1,-7/2) are two other points on the line.
You can surely find another point on the line working along the same line.
To find the equation of the line given a point (0,-5) and slope m=3/2, we can use the point-slope form of a linear equation (y - y1) = m(x - x1), where (x1, y1) is the given point and m is the slope.
a) Equation of the line:
Using the point-slope form, we have:
(y - (-5)) = (3/2)(x - 0)
Simplifying this equation, we get:
y + 5 = (3/2)x
To write it in the standard form, we need to get rid of the fraction. Multiplying both sides of the equation by 2, we have:
2(y + 5) = 2(3/2)x
2y + 10 = 3x
So, the equation of the line in standard form is: 3x - 2y - 10 = 0.
b) Three other points that go through the line:
One way to find other points that lie on the line is to substitute different values of x and solve for y.
Let's choose x = 1:
3(1) - 2y - 10 = 0
3 - 2y = 10
-2y = 10 - 3
-2y = 7
y = -7/2
So, one point that lies on the line is (1, -7/2).
Similarly, let's choose x = -1:
3(-1) - 2y - 10 = 0
-3 - 2y = 10
-2y = 13
y = -13/2
Another point on the line is (-1, -13/2).
For one more point, let's choose x = 2:
3(2) - 2y - 10 = 0
6 - 2y = 10
-2y = 4
y = -2
Therefore, another point on the line is (2, -2).
So, three other points that go through the line are (1, -7/2), (-1, -13/2), and (2, -2).