Answer:
The linear equation with given slope and y-intercept is:
Option 1: 
Step-by-step explanation:
The slope-intercept form of equation is given by:
Here
m is the slope of the line and b is the y-intercept.
Given that
Slope of line is 1/2 so m = 1/2
And y-intercept is on origin so b = 0
Putting the values we get
Hence,
The linear equation with given slope and y-intercept is:
Option 1:
Answer:
46
Step-by-step explanation:
For the value of y, substitute x = 28 into the equation.
2x + 3y = 194
2(28) + 3(y) = 194
56 + 3y = 194
3y = 194 - 56
3y = 138
dividing bothsides by 3
y = 46
1.b)
Fred has F cards. Bill has B cards. Tim has T cards.
B + F + T = 167
B = 5F
T = 4F - 3
5F + F + 4F - 3 = 167
10F - 3 = 167
10F = 170
F = 17
Fred has 17 cards.
B = 5F = 5(17) = 85
Bill has 85 cards.
T = 4F - 3 = 4(17) - 3 = 65
Tim has 65 cards.
2.a)
length = L
width = W
L = W + 5
perimeter = 2L + 2W = 168
2L + 2W = 168
2(W + 5) + 2W = 168
2W + 10 + 2W = 168
4W = 158
W = 39.5
L = W + 5 = 39.5 + 5 = 44.5
Length = 44.5 inches
Width = 39.5 inches
2.b)
Original rectangle:
width = W
length = 2W
New rectangle:
width = W - 1
length = 2W + 4
perimeter = 198 inches
perimeter = 2L + 2W = 198
2(2W + 4) + 2(W - 1) = 198
4W + 8 + 2W - 2 = 198
6W + 6 = 198
6W = 192
W = 32
L = 2W = 64
width = 32 inches
length = 64 inches
3.a)
Now:
Sam's age = S
John's age = 3S
In 5 years:
John's age = 3S + 5
Sam's age = S + 5
3S + 5 = 2(S + 5)
3S + 5 = 2S + 10
S = 5
Sam's age is 5.
John's age is 15.
This is all I have time for now. Post the rest of the problems in a different post, and I'll try to help later.
