Answer:
6) a) y = −7/2 x , b) y = −1/2 x , c) y = −5/4 x , d) y = −17/10 x
Step-by-step explanation:
For question 5 it needs to have the input and output values or having a domain and range value. So it can't be solved.
(there's an error in this question)
As for question 6,
a) with coordinate (x,y) = (-2,7)
1. To find the equation of a line or gradient,
first find the slope via the formula: -> m = (y2-y1/x2-x1)
If we let (0,0) ➡️ (x1,y1) and
(-2,7) ➡️ (x2,y2) then,
m = (7-0/-2-0) = -7/2 ⬅️ This is the slope of the line/gradient
Now that we have found the slope we can find the equation via the point-slope formula:
(y−y1) = m(x−x1) ;
2. Substituting the slope = -7/2 for
m and any of the two coordinates given. I will use (0,0) be make things easier. We let (0,0) → (x1,y1)
Thus,
y−0 = −7/2 (x-0)
If we simplify this, we simply get
y = −7/2 x ← This is our equation for coordinate (-2,7)
b) with coordinate (x,y) = (2,-1)
1. To find the equation of a line or gradient,
first find the slope via the formula: -> m = (y2-y1/x2-x1)
If we let (0,0) ➡️ (x1,y1) and
(2,-1) ➡️ (x2,y2) then,
m = (-1-0/2-0) = -1/2 ⬅️ This is the slope of the line/gradient
Now that we have found the slope we can find the equation via the point-slope formula:
(y−y1) = m(x−x1) ;
2. Substituting the slope = -1/2 for
m and any of the two coordinates given. I will use (0,0) be make things easier. We let (0,0) → (x1,y1)
Thus,
y−0 = −1/2 (x-0)
If we simplify this, we simply get
y = −1/2 x ← This is our equation for coordinate (2,-1)
c) with coordinate (x,y) = (4,-5)
1. To find the equation of a line or gradient,
first find the slope via the formula: -> m = (y2-y1/x2-x1)
If we let (0,0) ➡️ (x1,y1) and
(2,-1) ➡️ (x2,y2) then,
m = (-5-0/4-0) = -5/4 ⬅️ This is the slope of the line/gradient
Now that we have found the slope we can find the equation via the point-slope formula:
(y−y1) = m(x−x1) ;
2. Substituting the slope = -5/4 for
m and any of the two coordinates given. I will use (0,0) be make things easier. We let (0,0) → (x1,y1)
Thus,
y−0 = −5/4 (x-0)
If we simplify this, we simply get
y = −5/4 x ← This is our equation for coordinate (4,-5)
d) with coordinate (x,y) = (10,-17)
1. To find the equation of a line or gradient,
first find the slope via the formula: -> m = (y2-y1/x2-x1)
If we let (0,0) ➡️ (x1,y1) and
(2,-1) ➡️ (x2,y2) then,
m = (-17-0/10-0) = -17/10 ⬅️ This is the slope of the line/gradient
Now that we have found the slope we can find the equation via the point-slope formula:
(y−y1) = m(x−x1) ;
2. Substituting the slope = -17/10 for
m and any of the two coordinates given. I will use (0,0) be make things easier. We let (0,0) → (x1,y1)
Thus,
y−0 = −17/10 (x-0)
If we simplify this, we simply get
y = −17/10 x ← This is our equation for coordinate (10,-17)
