Math / Algebra

Question2 Matching 1 point Find the slope of the line that passes through the points given in the first column and match them with the appropriate result. \begin{tabular}{|l|l|l|} \hline $(10,7)$ and $(1,2)$ \\ \hline $(9,9)$ and $(1,16)$ & \\ \hline \\ \hline $(8,3)$ and $(2,1)$ & \\ \hline \end{tabular}

Studdy Solution

STEP 1

What is this asking? We need to find the slope of a line connecting pairs of points! Watch out! Remember the slope formula and be careful with your signs when subtracting coordinates.

STEP 2

1. Calculate the slope for the first pair of points.
2. Calculate the slope for the second pair of points.
3. Calculate the slope for the third pair of points.

STEP 3

Alright, let's find the slope between $(10, 7)$ and $(1, 2)$ .
Remember, the slope, often denoted as $m$ , is the change in $y$ divided by the change in $x$ .
It's like figuring out how steep a hill is!

STEP 4

The formula for slope is $m = \frac{y_2 - y_1}{x_2 - x_1}$ .
Let's plug in our values.
We'll call $(10, 7)$ our first point $(x_1, y_1)$ and $(1, 2)$ our second point $(x_2, y_2)$ .

STEP 5

So, we have $m = \frac{2 - 7}{1 - 10} = \frac{-5}{-9}$ .

STEP 6

Dividing a negative number by a negative number gives us a positive number.
So, $m = \frac{5}{9}$ .
The slope for the first pair of points is $\frac{5}{9}$ !

STEP 7

Now, let's tackle the second pair: $(9, 9)$ and $(1, 16)$ .
We'll use the same slope formula: $m = \frac{y_2 - y_1}{x_2 - x_1}$ .

STEP 8

Let $(9, 9)$ be $(x_1, y_1)$ and $(1, 16)$ be $(x_2, y_2)$ .
Plugging in the values, we get $m = \frac{16 - 9}{1 - 9} = \frac{7}{-8}$ .

STEP 9

So, the slope for the second pair is $-\frac{7}{8}$ .

STEP 10

Finally, let's find the slope between $(8, 3)$ and $(2, 1)$ .
Remember, our trusty formula: $m = \frac{y_2 - y_1}{x_2 - x_1}$ .

STEP 11

Let $(8, 3)$ be $(x_1, y_1)$ and $(2, 1)$ be $(x_2, y_2)$ .
Substituting the values, we have $m = \frac{1 - 3}{2 - 8} = \frac{-2}{-6}$ .

STEP 12

Simplifying, we get $m = \frac{1}{3}$ .
The slope for the third pair is $\frac{1}{3}$ !

STEP 13

The slope between $(10, 7)$ and $(1, 2)$ is $\frac{5}{9}$ .
The slope between $(9, 9)$ and $(1, 16)$ is $-\frac{7}{8}$ .
The slope between $(8, 3)$ and $(2, 1)$ is $\frac{1}{3}$ .

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Studdy Solution

STEP 1

What is this asking? We need to find the slope of a line connecting pairs of points! Watch out! Remember the slope formula and be careful with your signs when subtracting coordinates.

STEP 2

1. Calculate the slope for the first pair of points.
2. Calculate the slope for the second pair of points.
3. Calculate the slope for the third pair of points.

STEP 3

Alright, let's find the slope between $(10, 7)$ and $(1, 2)$ .
Remember, the slope, often denoted as $m$ , is the change in $y$ divided by the change in $x$ .
It's like figuring out how steep a hill is!

STEP 4

The formula for slope is $m = \frac{y_2 - y_1}{x_2 - x_1}$ .
Let's plug in our values.
We'll call $(10, 7)$ our first point $(x_1, y_1)$ and $(1, 2)$ our second point $(x_2, y_2)$ .

STEP 5

So, we have $m = \frac{2 - 7}{1 - 10} = \frac{-5}{-9}$ .

STEP 6

Dividing a negative number by a negative number gives us a positive number.
So, $m = \frac{5}{9}$ .
The slope for the first pair of points is $\frac{5}{9}$ !

STEP 7

Now, let's tackle the second pair: $(9, 9)$ and $(1, 16)$ .
We'll use the same slope formula: $m = \frac{y_2 - y_1}{x_2 - x_1}$ .

STEP 8

Let $(9, 9)$ be $(x_1, y_1)$ and $(1, 16)$ be $(x_2, y_2)$ .
Plugging in the values, we get $m = \frac{16 - 9}{1 - 9} = \frac{7}{-8}$ .

STEP 9

So, the slope for the second pair is $-\frac{7}{8}$ .

STEP 10

Finally, let's find the slope between $(8, 3)$ and $(2, 1)$ .
Remember, our trusty formula: $m = \frac{y_2 - y_1}{x_2 - x_1}$ .

STEP 11

Let $(8, 3)$ be $(x_1, y_1)$ and $(2, 1)$ be $(x_2, y_2)$ .
Substituting the values, we have $m = \frac{1 - 3}{2 - 8} = \frac{-2}{-6}$ .

STEP 12

Simplifying, we get $m = \frac{1}{3}$ .
The slope for the third pair is $\frac{1}{3}$ !

STEP 13

The slope between $(10, 7)$ and $(1, 2)$ is $\frac{5}{9}$ .
The slope between $(9, 9)$ and $(1, 16)$ is $-\frac{7}{8}$ .
The slope between $(8, 3)$ and $(2, 1)$ is $\frac{1}{3}$ .

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Studdy Solution

STEP 1

What is this asking? We need to find the slope of a line connecting pairs of points! Watch out! Remember the slope formula and be careful with your signs when subtracting coordinates.

STEP 2

1. Calculate the slope for the first pair of points.2. Calculate the slope for the second pair of points.3. Calculate the slope for the third pair of points.

STEP 3

Alright, let's find the slope between (10,7)(10, 7)(10,7) and (1,2)(1, 2)(1,2).Remember, the slope, often denoted as mmm, is the **change in** yyy divided by the **change in** xxx.It's like figuring out how steep a hill is!

STEP 4

The formula for slope is m=y2−y1x2−x1m = \frac{y_2 - y_1}{x_2 - x_1}m=x2​−x1​y2​−y1​​.Let's plug in our values.We'll call (10,7)(10, 7)(10,7) our **first point** (x1,y1)(x_1, y_1)(x1​,y1​) and (1,2)(1, 2)(1,2) our **second point** (x2,y2)(x_2, y_2)(x2​,y2​).

STEP 5

So, we have m=2−71−10=−5−9m = \frac{2 - 7}{1 - 10} = \frac{-5}{-9}m=1−102−7​=−9−5​.

STEP 6

Dividing a negative number by a negative number gives us a positive number.So, m=59m = \frac{5}{9}m=95​.The slope for the first pair of points is 59\frac{5}{9}95​!

STEP 7

Now, let's tackle the second pair: (9,9)(9, 9)(9,9) and (1,16)(1, 16)(1,16).We'll use the same slope formula: m=y2−y1x2−x1m = \frac{y_2 - y_1}{x_2 - x_1}m=x2​−x1​y2​−y1​​.

STEP 8

Let (9,9)(9, 9)(9,9) be (x1,y1)(x_1, y_1)(x1​,y1​) and (1,16)(1, 16)(1,16) be (x2,y2)(x_2, y_2)(x2​,y2​).Plugging in the values, we get m=16−91−9=7−8m = \frac{16 - 9}{1 - 9} = \frac{7}{-8}m=1−916−9​=−87​.

STEP 9

So, the slope for the second pair is −78-\frac{7}{8}−87​.

STEP 10

Finally, let's find the slope between (8,3)(8, 3)(8,3) and (2,1)(2, 1)(2,1).Remember, our trusty formula: m=y2−y1x2−x1m = \frac{y_2 - y_1}{x_2 - x_1}m=x2​−x1​y2​−y1​​.

STEP 11

Let (8,3)(8, 3)(8,3) be (x1,y1)(x_1, y_1)(x1​,y1​) and (2,1)(2, 1)(2,1) be (x2,y2)(x_2, y_2)(x2​,y2​).Substituting the values, we have m=1−32−8=−2−6m = \frac{1 - 3}{2 - 8} = \frac{-2}{-6}m=2−81−3​=−6−2​.

STEP 12

Simplifying, we get m=13m = \frac{1}{3}m=31​.The slope for the third pair is 13\frac{1}{3}31​!

STEP 13

The slope between (10,7)(10, 7)(10,7) and (1,2)(1, 2)(1,2) is 59\frac{5}{9}95​.The slope between (9,9)(9, 9)(9,9) and (1,16)(1, 16)(1,16) is −78-\frac{7}{8}−87​.The slope between (8,3)(8, 3)(8,3) and (2,1)(2, 1)(2,1) is 13\frac{1}{3}31​.

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1. Calculate the slope for the first pair of points.
2. Calculate the slope for the second pair of points.
3. Calculate the slope for the third pair of points.

Alright, let's find the slope between $(10, 7)$ and $(1, 2)$ .
Remember, the slope, often denoted as $m$ , is the change in $y$ divided by the change in $x$ .
It's like figuring out how steep a hill is!

The formula for slope is $m = \frac{y_2 - y_1}{x_2 - x_1}$ .
Let's plug in our values.
We'll call $(10, 7)$ our first point $(x_1, y_1)$ and $(1, 2)$ our second point $(x_2, y_2)$ .

So, we have $m = \frac{2 - 7}{1 - 10} = \frac{-5}{-9}$ .

Dividing a negative number by a negative number gives us a positive number.
So, $m = \frac{5}{9}$ .
The slope for the first pair of points is $\frac{5}{9}$ !

Now, let's tackle the second pair: $(9, 9)$ and $(1, 16)$ .
We'll use the same slope formula: $m = \frac{y_2 - y_1}{x_2 - x_1}$ .

Let $(9, 9)$ be $(x_1, y_1)$ and $(1, 16)$ be $(x_2, y_2)$ .
Plugging in the values, we get $m = \frac{16 - 9}{1 - 9} = \frac{7}{-8}$ .

So, the slope for the second pair is $-\frac{7}{8}$ .

Finally, let's find the slope between $(8, 3)$ and $(2, 1)$ .
Remember, our trusty formula: $m = \frac{y_2 - y_1}{x_2 - x_1}$ .

Let $(8, 3)$ be $(x_1, y_1)$ and $(2, 1)$ be $(x_2, y_2)$ .
Substituting the values, we have $m = \frac{1 - 3}{2 - 8} = \frac{-2}{-6}$ .

Simplifying, we get $m = \frac{1}{3}$ .
The slope for the third pair is $\frac{1}{3}$ !

The slope between $(10, 7)$ and $(1, 2)$ is $\frac{5}{9}$ .
The slope between $(9, 9)$ and $(1, 16)$ is $-\frac{7}{8}$ .
The slope between $(8, 3)$ and $(2, 1)$ is $\frac{1}{3}$ .