and y-intercept.
the equation with its graph. identify the slope
1. $y = -\frac{1}{2}x + 5$
2. $y = -3x - 1$
3. $y = \frac{2}{3}x + 2$
find the slope and the y-intercept of the graph of
the linear equation.
4. $y = x + 4$
5. $y = -8x + 3$
6. $y = -\frac{5}{7}x - 2$
7. $y = 1.75x - 1$
8. $y - 2 = 6x$
9. $y + 7 = \frac{1}{9}x$
10. your friend finds the slope and y-intercept of the graph of the equation
$y = -5x + 4$. is your friend correct? explain your reasoning.
$y = -5x + 4$; the slope is 4 and the y-intercept is $-5$.
graph the linear equation. identify the x-intercept.
11. $y = 3x - 6$
12. $y = -\frac{1}{4}x + 12$
13. $y = 3.2x + 9.6$
14. $y - 2 = 5x$
15. the amount of fertilizer $y$ (in cups) that is needed for $x$ square feet of grass
is $y = \frac{1}{4}x$.
a. graph the equation.
b. interpret the slope and y-intercept.

Question

and y-intercept.
the equation with its graph. identify the slope
1. $y = -\frac{1}{2}x + 5$
2. $y = -3x - 1$
3. $y = \frac{2}{3}x + 2$
find the slope and the y-intercept of the graph of
the linear equation.
4. $y = x + 4$
5. $y = -8x + 3$
6. $y = -\frac{5}{7}x - 2$
7. $y = 1.75x - 1$
8. $y - 2 = 6x$
9. $y + 7 = \frac{1}{9}x$
10. your friend finds the slope and y-intercept of the graph of the equation
$y = -5x + 4$. is your friend correct? explain your reasoning.
$y = -5x + 4$; the slope is 4 and the y-intercept is $-5$.
graph the linear equation. identify the x-intercept.
11. $y = 3x - 6$
12. $y = -\frac{1}{4}x + 12$
13. $y = 3.2x + 9.6$
14. $y - 2 = 5x$
15. the amount of fertilizer $y$ (in cups) that is needed for $x$ square feet of grass
is $y = \frac{1}{4}x$.
    a. graph the equation.
    b. interpret the slope and y-intercept.

Accepted Answer

### Question 10
# Explanation:
## Step 1: Recall the slope - intercept form
The slope - intercept form of a linear equation is $y = mx + b$, where $m$ is the slope and $b$ is the $y$ - intercept.
## Step 2: Analyze the given equation
For the equation $y=-5x + 4$, comparing it with $y=mx + b$, we can see that $m=-5$ (the coefficient of $x$) and $b = 4$ (the constant term).
## Step 3: Compare with the friend's answer
The friend said that the slope is 4 and the $y$ - intercept is - 5, which is the reverse of the correct values.

# Answer:
The friend is not correct. For the linear equation $y = mx + b$ (slope - intercept form), in the equation $y=-5x + 4$, the slope $m=-5$ (the coefficient of $x$) and the $y$ - intercept $b = 4$ (the constant term). The friend has swapped the values of the slope and the $y$ - intercept.

### Question 11
# Explanation:
## Step 1: Find the $y$ - intercept
For the equation $y = 3x-6$, the slope - intercept form is $y=mx + b$. When $x = 0$, $y=3(0)-6=-6$. So the $y$ - intercept is - 6.
## Step 2: Find the $x$ - intercept
To find the $x$ - intercept, we set $y = 0$ in the equation $y=3x - 6$. So, $0=3x-6$.
## Step 3: Solve for $x$
Add 6 to both sides of the equation $0 = 3x-6$: $3x=6$.
Divide both sides by 3: $x=\frac{6}{3}=2$. So the $x$ - intercept is 2.

# Answer:
$y$ - intercept: $-6$; $x$ - intercept: $2$

### Question 12
# Explanation:
## Step 1: Find the $y$ - intercept
For the equation $y=-\frac{1}{4}x + 12$, using the slope - intercept form $y = mx + b$, when $x = 0$, $y=-\frac{1}{4}(0)+12 = 12$. So the $y$ - intercept is 12.
## Step 2: Find the $x$ - intercept
Set $y = 0$ in the equation $y=-\frac{1}{4}x + 12$. Then $0=-\frac{1}{4}x+12$.
## Step 3: Solve for $x$
Subtract 12 from both sides: $-\frac{1}{4}x=-12$.
Multiply both sides by - 4: $x=(-12)	imes(-4)=48$. So the $x$ - intercept is 48.

# Answer:
$y$ - intercept: $12$; $x$ - intercept: $48$

### Question 13
# Explanation:
## Step 1: Find the $y$ - intercept
For the equation $y = 3.2x+9.6$, using the slope - intercept form $y=mx + b$, when $x = 0$, $y=3.2(0)+9.6 = 9.6$. So the $y$ - intercept is 9.6.
## Step 2: Find the $x$ - intercept
Set $y = 0$ in the equation $y=3.2x + 9.6$. Then $0=3.2x+9.6$.
## Step 3: Solve for $x$
Subtract 9.6 from both sides: $3.2x=-9.6$.
Divide both sides by 3.2: $x=\frac{-9.6}{3.2}=-3$. So the $x$ - intercept is - 3.

# Answer:
$y$ - intercept: $9.6$; $x$ - intercept: $-3$

### Question 14
# Explanation:
## Step 1: Rewrite the equation in slope - intercept form
The equation $y - 2=5x$ can be rewritten as $y=5x + 2$ (by adding 2 to both sides).
## Step 2: Find the $y$ - intercept
For the equation $y=5x + 2$, using the slope - intercept form $y=mx + b$, when $x = 0$, $y=5(0)+2 = 2$. So the $y$ - intercept is 2.
## Step 3: Find the $x$ - intercept
Set $y = 0$ in the equation $y=5x + 2$. Then $0=5x+2$.
## Step 4: Solve for $x$
Subtract 2 from both sides: $5x=-2$.
Divide both sides by 5: $x=-\frac{2}{5}=-0.4$. So the $x$ - intercept is $-\frac{2}{5}$ (or - 0.4).

# Answer:
$y$ - intercept: $2$; $x$ - intercept: $-\frac{2}{5}$ (or - 0.4)

### Question 15
#### Part (a)
To graph the equation $y=\frac{1}{4}x$:
- The slope - intercept form is $y = mx + b$, where $m=\frac{1}{4}$ and $b = 0$ (since there is no constant term).
- Plot the $y$ - intercept: Since $b = 0$, the line passes through the origin $(0,0)$.
- Use the slope to find another point. The slope $m=\frac{1}{4}$ means that for every 4 units we move to the right (increase in $x$ by 4), we move up 1 unit (increase in $y$ by 1). So from the origin $(0,0)$, if we move $x = 4$, then $y=\frac{1}{4}(4)=1$, so the point $(4,1)$ is also on the line. Draw a straight line through the points $(0,0)$ and $(4,1)$.

#### Part (b)
# Explanation:
## Step 1: Interpret the slope
The slope $m=\frac{1}{4}$ in the equation $y=\frac{1}{4}x$ (slope - intercept form $y = mx + b$ with $b = 0$) means that for each additional square foot of grass ($x$ increases by 1), the amount of fertilizer needed ($y$) increases by $\frac{1}{4}$ cups.
## Step 2: Interpret the $y$ - intercept
The $y$ - intercept $b = 0$ means that when the area of the grass $x = 0$ (no grass), the amount of fertilizer needed $y = 0$ cups.

# Answer:
a. To graph $y=\frac{1}{4}x$, plot the origin $(0,0)$ and the point $(4,1)$ (using the slope $\frac{1}{4}$: rise = 1, run = 4) and draw a straight line through them.
b. The slope $\frac{1}{4}$ means that for each square foot increase in the area of the grass, the amount of fertilizer needed increases by $\frac{1}{4}$ cups. The $y$ - intercept is 0, which means that 0 cups of fertilizer are needed for 0 square feet of grass (when there is no grass, no fertilizer is needed).

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QUESTION IMAGE

Question

Explanation:

Question 10

Step 1: Recall the slope - intercept form

Step 2: Analyze the given equation

Step 3: Compare with the friend's answer

Step 1: Find the $y$ - intercept

Step 2: Find the $x$ - intercept

Step 3: Solve for $x$

Step 1: Find the $y$ - intercept

Step 2: Find the $x$ - intercept

Step 3: Solve for $x$

Answer:

Question 11