Answer:
1. y = 2x + 1
2. the equation of the line is, y = -5/2x + 7
3. the equation of the line is, y = 5/2x - 5
4. the equation of the line is, y = 3/2x + 6
5. the equation of the line is, y = x - 9
6. the equation of the line is, y = -2x - 1
7. the equation of the line is, y = -3/7x + 48/7
8. the equation of the line is, y = -3x + 13
Explanation:
equation of the line is, y = mx + b
where slope, m = y2 - y1 / x2 - x1
b is the constant
x, y are the given points
1)
p1 = (0, 1), p2 = (2, 5)
m = 5 - 1 / 2 - 0 = 4/2 = 2
y = mx + b
let's take any point from the given two points to find the constant b
i am taking p1 (0, 1)
1 = 2(0) + b
1 = 0 + b
b = 1
thus, the equation of the line is: y = 2x + 1
2)
p1 = (2, 0), p2 = (0, 5)
m = 5 - 0 / 0 - 2 = 5/-2 = -5/2
let's take p1(2, 0) x,y coordinates to find b
2 = -5/2(2) + b
2 = -5 + b
2 + 5 = b
b = 7
thus, the equation of the line is, y = -5/2x + 7
3)
p1 = (0, -5), p2 = (2, 0)
m = y2 - y1 / x2 - x1
m = 0 + 5 / 2 - 0 = 5/2
let's take p1 (0, -5) to find b
-5 = 5/2(0) + b
b = -5
thus, the equation of the line is, y = 5/2x - 5
4)
p1 = (-2, 3), p2 = (0, 6)
m = 6 - 3 / 0 + 2 = 3/2
let's take p1(-2, 3) to find b
3 = 3/2(-2) + b
3 = -3 + b
3 + 3 = b
b = 6
thus, the equation of the line is, y = 3/2x + 6
5)
p1 = (4, -5), p2 = (11, 2)
m = 2 + 5 / 11 - 4 = 7/7 = 1
let's take p1 = (4, -5) to find b,
-5 = 1(4) + b
-5 - 4 = b
b = -9
thus, the equation of the line is, y = x - 9
6)
p1 = (0, -1), p2 = (-1, 1)
m = 1 + 1 / -1 - 0 = 2/-1 = -2
let's take p1 = (0, -1) to find b
-1 = -2(0) + b
-1 = b
thus, the equation of the line is, y = -2x - 1
7)
p1 = (16, 0), p2 = (2, 6)
m = 6 - 0 / 2 - 16 = 6/-14 = -3/7
let's take p1 = (16, 0) to find b
0 = -3/7(16) + b
48/7 = b
thus, the equation of the line is, y = -3/7x + 48/7
8)
p1 = (3, 4), p2 = (2, 7)
m = 7 - 4 / 2 - 3 = 3/-1 = -3
let's take p1 = (3, 4) to find b
4 = -3(3) + b
4 + 9 = b
b = 13
thus, the equation of the line is, y = -3x + 13