Explanation:
again, I can only assume that the equations are requested in slope/intercept form :
y = ax + b
"a" being the slope, "b" being the y- intercept (the y value for x = 0).
the slope is always (y coordinate change / x coordinate change).
"b" we get then by using the coordinates of one point in the equation.
a.
A
(35, 168) to (57, 278)
x changes by +23 (35 to 57).
y changes by +110 (168 to 278).
slope is +110/+23
y = 110/23 x + b
168 = 110/23 × 35 + b | ×23
3864 = 110×35 + 23b = 3850 + 23b
14 = 23b
b = 14/23
y = 110/23 x + 14/23 = 1/23 × (110x + 14)
(35, 168) to (79, 190)
x changes by +44 (35 to 79).
y changes by +22 (168 to 190).
slope is +22/+44 = 1/2
y = 1/2 x + b
168 = 1/2 × 35 + b | ×2
336 = 35 + 2b
301 = 2b
b = 301/2
y = 1/2 x + 301/2 = 1/2 × (x + 301)
(35, 168) to (123, 168)
x changes by +88 (35 to 123).
y changes by 0 (168 to 168).
slope is 0/+88 = 0
y = 0x + b = b
168 = b
y = 168
(79, 190) to (123, 168)
x changes by +44 (79 to 123).
y changes by -22 (190 to 168).
slope is -22/+44 = -1/2
y = -1/2 x + b
190 = -1/2 × 79 + b | ×2
380 = -79 + 2b
459 = 2b
b = 459/2
y = -1/2 x + 459/2 = 1/2 × (-x + 459)
B
(21, 141) to (64, 55)
x changes by +43 (21 to 64).
y changes by -86 (141 to 55).
slope is -86/+43 = -2
y = -2x + b
141 = -2 × 21 + b
141 = -42 + b
183 = b
y = -2x + 183
(64, 55) to (128, 87)
x changes by +64 (64 to 128).
y changes by +32 (55 to 87).
slope is +32/+64 = 1/2
y = 1/2 x + b
55 = 1/2 × 64 + b
55 = 32 + b
23 = b
y = 1/2 x + 23
(86, 66) to (95, 3)
x changes by +9 (86 to 95).
y changes by -63 (66 to 3).
slope is -63/+9 = -7
y = -7x + b
66 = -7 × 86 + b
66 = -602 + b
668 = b
y = -7x + 668
(89, 45) to (130, 45)
x changes by +41 (89 to 130).
y changes by 0 (45 to 45).
slope is 0/+41 = 0
y = 0x + b
45 = 0 × 35 + b
45 = b
y = 45
b.
the domain is the interval of the valid x values. the range is the interval of the valid y values.
y = 110/23 x + 14/23 = 1/23 × (110x + 14)
domain based on the points' coordinates :
35 <= x <= 57
range based on the points' coordinates :
168 <= y <= 278
the line is increasing.
y = 1/2 x + 301/2 = 1/2 × (x + 301)
domain based on the points' coordinates :
35 <= x <= 79
range based on the points' coordinates :
168 <= y <= 190
the line is increasing.
y = 168
domain based on the points' coordinates :
35 <= x <= 123
range based on the points' coordinates :
y = 168
the line is a flat, horizontal line.
y = -1/2 x + 459/2 = 1/2 × (-x + 459)
domain based on the points' coordinates :
79 <= x <= 123
range based on the points' coordinates :
168 <= y <= 190
the line is decreasing.
y = -2x + 183
domain based on the points' coordinates :
21 <= x <= 64
range based on the points' coordinates :
55 <= y <= 141
the line is decreasing.
y = 1/2 x + 23
domain based on the points' coordinates :
64 <= x <= 128
range based on the points' coordinates :
55 <= y <= 87
the line is increasing.
y = -7x + 668
domain based on the points' coordinates :
86 <= x <= 95
range based on the points' coordinates :
3 <= y <= 66
the line is decreasing.
y = 45
domain based on the points' coordinates :
89 <= x <= 130
range based on the points' coordinates :
y = 45
the line is a flat, horizontal line.