kuta software - infinite algebra 1
finding slope from an equation
find the slope of each line.
1) ( y = -\frac{5}{2}x - 3 )
2) ( y = -\frac{4}{3}x - 1 )
3) ( y = -x + 3 )
4) ( y = -4x - 1 )
5) ( 2x - y = 1 )
6) ( x + 2y = -8 )
7) ( 8x + 3y = -9 )
8) ( 4x + 5y = -10 )
9) ( x - y = -2 )
10) ( 4x - 3y = 9 )
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find y - intercept (handwritten)

Question

Accepted Answer

Let's solve each problem step by step. The general form of a linear equation is $ y = mx + b $, where $ m $ is the slope. For equations not in this form, we can rearrange them to solve for $ y $.

### Problem 1: $ y = -\frac{5}{2}x - 3 $
## Step 1: Identify the slope
The equation is in slope - intercept form ($ y=mx + b $). Here, $ m = -\frac{5}{2} $.
# Answer: $ -\frac{5}{2} $

### Problem 2: $ y=-\frac{4}{3}x - 1 $
## Step 1: Identify the slope
The equation is in slope - intercept form. So, $ m=-\frac{4}{3} $.
# Answer: $ -\frac{4}{3} $

### Problem 3: $ y=-x + 3 $
## Step 1: Identify the slope
We can write $ y=-x + 3$ as $ y=(-1)x+3 $. In the slope - intercept form, $ m = - 1 $.
# Answer: $ - 1 $

### Problem 4: $ y=-4x - 1 $
## Step 1: Identify the slope
The equation is in slope - intercept form. So, $ m=-4 $.
# Answer: $ - 4 $

### Problem 5: $ 2x-y = 1 $
## Step 1: Rearrange the equation to slope - intercept form
Subtract $ 2x $ from both sides: $ -y=-2x + 1 $
Multiply both sides by - 1: $ y = 2x-1 $
## Step 2: Identify the slope
In the form $ y = mx + b $, $ m = 2 $.
# Answer: $ 2 $

### Problem 6: $ x + 2y=-8 $ (Find y - intercept)
## Step 1: Rearrange to slope - intercept form
Subtract $ x $ from both sides: $ 2y=-x - 8 $
Divide both sides by 2: $ y=-\frac{1}{2}x-4 $
## Step 2: Identify the y - intercept
In the slope - intercept form $ y = mx + b $, the y - intercept $ b=-4 $.
# Answer: $ - 4 $

### Problem 7: $ 8x + 3y=-9 $
## Step 1: Rearrange to slope - intercept form
Subtract $ 8x $ from both sides: $ 3y=-8x - 9 $
Divide both sides by 3: $ y=-\frac{8}{3}x-3 $
## Step 2: Identify the slope
In the form $ y = mx + b $, $ m = -\frac{8}{3} $.
# Answer: $ -\frac{8}{3} $

### Problem 8: $ 4x + 5y=-10 $
## Step 1: Rearrange to slope - intercept form
Subtract $ 4x $ from both sides: $ 5y=-4x - 10 $
Divide both sides by 5: $ y=-\frac{4}{5}x-2 $
## Step 2: Identify the slope
In the form $ y = mx + b $, $ m = -\frac{4}{5} $.
# Answer: $ -\frac{4}{5} $

### Problem 9: $ x - y=-2 $
## Step 1: Rearrange to slope - intercept form
Subtract $ x $ from both sides: $ -y=-x - 2 $
Multiply both sides by - 1: $ y=x + 2 $
## Step 2: Identify the slope
In the form $ y = mx + b $, $ m = 1 $.
# Answer: $ 1 $

### Problem 10: $ 4x-3y = 9 $
## Step 1: Rearrange to slope - intercept form
Subtract $ 4x $ from both sides: $ -3y=-4x + 9 $
Divide both sides by - 3: $ y=\frac{4}{3}x-3 $
## Step 2: Identify the slope
In the form $ y = mx + b $, $ m=\frac{4}{3} $.
# Answer: $ \frac{4}{3} $

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QUESTION IMAGE

Question

Explanation:

Problem 1: \( y = -\frac{5}{2}x - 3 \)

Step 1: Identify the slope

Answer:

Problem 2: \( y=-\frac{4}{3}x - 1 \)

Step 1: Identify the slope