Реши задание на изображении

Here is the full solution in English.

In \(y=mx+b\), \(m\) is the slope — how much \(y\) changes when \(x\) increases by \(1\). \(b\) is the \(y\)-intercept — the value of \(y\) when \(x=0\).

1. First page

• Slope: \(-\frac52=-2.5\).
  Meaning: the balance decreases by $2.50 for each school day.
• \(y\)-intercept: \(40\), at \((0,40)\).
  Meaning: the card had $40 on day 0.
• For \(b=40-2.50d\):
  • slope \(=-2.50\);
  • \(y\)-intercept \(=40\).

Check: when \(d=2\),
\[ b=40-2.50\cdot2=35, \] which matches the point \((2,35)\).

2. Problem 1

\[ 5x-2y=20 \] \[ -2y=20-5x \] \[ y=\frac52x-10 \]

The slope is the coefficient of \(x\):

\[ \boxed{\frac52} \]

Answer: C) \(\frac52\).

3. Problem 2

Find the \(y\)-intercept by setting \(x=0\).

a) \[ y=6x+2 \] When \(x=0\), \(y=2\).

\[ \boxed{2} \]

b) \[ 10x+5y=30 \] When \(x=0\): \[ 5y=30 \Rightarrow y=6. \]

\[ \boxed{6} \]

c) \[ y-6=2(3x-4) \] \[ y=6+6x-8=6x-2 \] When \(x=0\): \[ \boxed{-2} \]

4. Problem 3

Han solved: \[ 10x+4y=20 \] \[ 4y=20-10x \]

He needs to divide every term by \(4\): \[ y=5-\frac{10}{4}x=5-2.5x \]

But Han wrote: \[ y=5-10x \]

So his mistake was: he did not divide \(10x\) by \(4\).

Correct intercepts:

• \(x\)-intercept: set \(y=0\) \[ 10x=20 \Rightarrow x=2 \] So \((2,0)\).

• \(y\)-intercept: set \(x=0\) \[ 4y=20 \Rightarrow y=5 \] So \((0,5)\).

Answer:
\(x\)-intercept: \((2,0)\)
\(y\)-intercept: \((0,5)\)

Han’s \(y\)-intercept was correct, but his \(x\)-intercept was not.

5. Problem 4

\[ 12=3x+4y \] \[ 4y=-3x+12 \] \[ y=-\frac34x+3 \]

The slope is negative: \[ -\frac34 \]

The \(y\)-intercept is \(3\), and the \(x\)-intercept is \(4\).

The correct graph is A, because it is the only line with a negative slope.

6. Problem 5

A nickel is \(5\) cents, and a dime is \(10\) cents. The total is \(125\) cents.

Let \(n\) be the number of nickels and \(d\) the number of dimes.

a) For example, \(15\) nickels and \(5\) dimes: \[ 15\cdot5+5\cdot10=75+50=125 \]

b) The equation is: \[ 5n+10d=125 \] or, dividing by \(5\): \[ n+2d=25 \]

If the coordinates are written as \((n,d)\), then the equation is: \[ 5x+10y=125 \]

c) The point \((13,6)\) means 13 nickels and 6 dimes: \[ 13\cdot5+6\cdot10=65+60=125 \] So it makes $1.25.

d) Yes, \((13,6)\) is a solution because: \[ 13+2\cdot6=13+12=25 \]

So the final answers are:

\[ \boxed{\text{1. Slope } \frac52 \text{; answer C}} \]

\[ \boxed{\text{2. a) }2,\quad \text{b) }6,\quad \text{c) }-2} \]

\[ \boxed{\text{3. Han did not divide }10x\text{ by }4;\quad (2,0),\ (0,5)} \]

\[ \boxed{\text{4. Graph A; } y=-\frac34x+3} \]

\[ \boxed{\text{5. }5n+10d=125;\quad (13,6)\text{ means 13 nickels and 6 dimes}} \]

Yes — the total value is:

\[ 13(0.05)+6(0.10)=0.65+0.60=1.25 \]

So it is $1.25.

Just be careful: the point \((13,6)\) itself represents 13 nickels and 6 dimes; their combined value is $1.25. And \((13,6)\) is a solution because:

\[ 5(13)+10(6)=125\text{ cents} \]

or

\[ 13+2(6)=25. \]

So for the last question: Yes, it is a solution, and the total value is $1.25.