practice
example 1
write an equation of a line in slope - intercept form with the given slope and y - intercept.
1. slope: 5, y - intercept: - 3
2. slope: - 2, y - intercept: 7
3. slope: - 6, y - intercept: - 2
4. slope: 7, y - intercept: 1
5. slope: 3, y - intercept: 2
6. slope: - 4, y - intercept: - 9
7. slope: 1, y - intercept: - 12
8. slope: 0, y - intercept: 8
example 2
write each equation in slope - intercept form.
9. - 10x + 2y = 12
10. 4y + 12x = 16
11. - 5x + 15y = - 30
12. 6x - 3y = - 18
13. - 2x - 8y = 24
14. - 4x - 10y = - 7

Question

Accepted Answer

Let's solve problem 9: $-10x + 2y = 12$ (writing in slope - intercept form $y=mx + b$, where $m$ is the slope and $b$ is the y - intercept)

# Explanation:
## Step 1: Isolate the $y$ - term
We start with the equation $-10x + 2y=12$. First, we add $10x$ to both sides of the equation to get the $y$ - term by itself.
$-10x + 2y+10x=12 + 10x$
Simplifying the left - hand side, $-10x+10x = 0$, so we have $2y=10x + 12$

## Step 2: Solve for $y$
Now, we divide every term in the equation $2y = 10x+12$ by 2 to solve for $y$.
$y=\frac{10x}{2}+\frac{12}{2}$
Simplifying the fractions, $\frac{10x}{2}=5x$ and $\frac{12}{2} = 6$. So $y = 5x+6$

Let's solve problem 10: $4y+12x = 16$

# Explanation:
## Step 1: Isolate the $y$ - term
Start with $4y + 12x=16$. Subtract $12x$ from both sides of the equation.
$4y+12x-12x=16 - 12x$
Simplifying the left - hand side, $12x-12x = 0$, so $4y=-12x + 16$

## Step 2: Solve for $y$
Divide every term in the equation $4y=-12x + 16$ by 4.
$y=\frac{-12x}{4}+\frac{16}{4}$
Simplifying the fractions, $\frac{-12x}{4}=-3x$ and $\frac{16}{4}=4$. So $y=-3x + 4$

Let's solve problem 11: $-5x + 15y=-30$

# Explanation:
## Step 1: Isolate the $y$ - term
Start with $-5x + 15y=-30$. Add $5x$ to both sides of the equation.
$-5x + 15y+5x=-30 + 5x$
Simplifying the left - hand side, $-5x + 5x=0$, so $15y=5x-30$

## Step 2: Solve for $y$
Divide every term in the equation $15y = 5x-30$ by 15.
$y=\frac{5x}{15}-\frac{30}{15}$
Simplifying the fractions, $\frac{5x}{15}=\frac{1}{3}x$ and $\frac{30}{15} = 2$. So $y=\frac{1}{3}x-2$

Let's solve problem 12: $6x-3y=-18$

# Explanation:
## Step 1: Isolate the $y$ - term
Start with $6x-3y=-18$. Subtract $6x$ from both sides of the equation.
$6x-3y-6x=-18 - 6x$
Simplifying the left - hand side, $6x-6x = 0$, so $-3y=-6x-18$

## Step 2: Solve for $y$
Divide every term in the equation $-3y=-6x - 18$ by $-3$.
$y=\frac{-6x}{-3}-\frac{18}{-3}$
Simplifying the fractions, $\frac{-6x}{-3}=2x$ and $\frac{-18}{-3}=6$. So $y = 2x+6$

Let's solve problem 13: $-2x-8y = 24$

# Explanation:
## Step 1: Isolate the $y$ - term
Start with $-2x-8y = 24$. Add $2x$ to both sides of the equation.
$-2x-8y + 2x=24 + 2x$
Simplifying the left - hand side, $-2x+2x = 0$, so $-8y=2x + 24$

## Step 2: Solve for $y$
Divide every term in the equation $-8y=2x + 24$ by $-8$.
$y=\frac{2x}{-8}+\frac{24}{-8}$
Simplifying the fractions, $\frac{2x}{-8}=-\frac{1}{4}x$ and $\frac{24}{-8}=-3$. So $y=-\frac{1}{4}x-3$

Let's solve problem 14: $-4x-10y=-7$

# Explanation:
## Step 1: Isolate the $y$ - term
Start with $-4x-10y=-7$. Add $4x$ to both sides of the equation.
$-4x-10y + 4x=-7 + 4x$
Simplifying the left - hand side, $-4x + 4x=0$, so $-10y=4x-7$

## Step 2: Solve for $y$
Divide every term in the equation $-10y=4x - 7$ by $-10$.
$y=\frac{4x}{-10}-\frac{-7}{10}$
Simplifying the fractions, $\frac{4x}{-10}=-\frac{2}{5}x$ and $\frac{-7}{-10}=\frac{7}{10}$. So $y=-\frac{2}{5}x+\frac{7}{10}$

Now, let's solve the slope - intercept form problems (Example 1):

### Problem 1: slope $m = 5$, y - intercept $b=-3$
The slope - intercept form is $y=mx + b$. Substitute $m = 5$ and $b=-3$ into the formula.
$y=5x-3$

### Problem 2: slope $m=-2$, y - intercept $b = 7$
Using $y=mx + b$, substitute $m=-2$ and $b = 7$.
$y=-2x + 7$

### Problem 3: slope $m=-6$, y - intercept $b=-2$
Using $y=mx + b$, substitute $m=-6$ and $b=-2$.
$y=-6x-2$

### Problem 4: slope $m = 7$, y - intercept $b = 1$
Using $y=mx + b$, substitute $m = 7$ and $b = 1$.
$y=7x + 1$

### Problem 5: slope $m = 3$, y - intercept $b = 2$
Using $y=mx + b$, substitute $m = 3$ and $b = 2$.
$y=3x + 2$

### Problem 6: slope $m=-4$, y - intercept $b=-9$
Using $y=mx + b$, substitute $m=-4$ and $b=-9$.
$y=-4x-9$

### Problem 7: slope $m = 1$, y - intercept $b=-12$
Using $y=mx + b$, substitute $m = 1$ and $b=-12$.
$y=x-12$

### Problem 8: slope $m = 0$, y - intercept $b = 8$
Using $y=mx + b$, substitute $m = 0$ and $b = 8$.
$y=0\times x+8=8$ (This is a horizontal line)

# Answers:

### Example 1 (Write equation in slope - intercept form):
1. $y = 5x-3$
2. $y=-2x + 7$
3. $y=-6x-2$
4. $y=7x + 1$
5. $y=3x + 2$
6. $y=-4x-9$
7. $y=x-12$
8. $y = 8$

### Example 2 (Write equation in slope - intercept form):
9. $y = 5x+6$
10. $y=-3x + 4$
11. $y=\frac{1}{3}x-2$
12. $y = 2x+6$
13. $y=-\frac{1}{4}x-3$
14. $y=-\frac{2}{5}x+\frac{7}{10}$

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QUESTION IMAGE

Question

Explanation:

Step 1: Isolate the \(y\) - term

Step 2: Solve for \(y\)

Step 1: Isolate the \(y\) - term

Step 2: Solve for \(y\)

Step 1: Isolate the \(y\) - term

Step 2: Solve for \(y\)

Answer:

Example 1 (Write equation in slope - intercept form):

Example 2 (Write equation in slope - intercept form):