Math / Algebra

QuestionQuestion Watch Video Show Examples
Find the x - and y -intercepts of the graph of $3 x-y=37$ . State each answer as an integer or an improper fraction in simplest form.
Answer Attempt 1 out of 2

Studdy Solution

STEP 1

What is this asking? We need to find the points where this line hits the x-axis and the y-axis! Watch out! Don't mix up the x and y intercepts!
Remember x-intercept means y is zero, and y-intercept means x is zero!

STEP 2

1. Find the x-intercept
2. Find the y-intercept

STEP 3

The x-intercept is where the line crosses the x-axis.
This happens when $y = 0$ !

STEP 4

Let's substitute $y = 0$ into our equation $3x - y = 37$ .
This gives us $3x - 0 = 37$ .

STEP 5

So, we have $3x = 37$ .
To isolate $x$ , we'll divide both sides by 3 (we're dividing to one to isolate $x$ ).
This gives us $x = \frac{37}{3}$ .
Boom!

STEP 6

Our x-intercept is $\left( \frac{37}{3}, 0 \right)$ .
Remember, the y-value is zero at the x-intercept!

STEP 7

The y-intercept is where the graph crosses the y-axis, which happens when $x = 0$ !

STEP 8

Now, we'll substitute $x = 0$ into our original equation $3x - y = 37$ .
This gives us $3 \cdot 0 - y = 37$ .

STEP 9

This simplifies to $-y = 37$ .
To get $y$ by itself, we'll multiply both sides by $-1$ .
This gives us $y = -37$ .
Awesome!

STEP 10

Our y-intercept is $(0, -37)$ .
Remember, the x-value is zero at the y-intercept!

STEP 11

The x-intercept is $\left( \frac{37}{3}, 0 \right)$ and the y-intercept is $(0, -37)$ .
We found where the line crosses both axes!

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QuestionQuestion Watch Video Show Examples
Find the x - and y -intercepts of the graph of $3 x-y=37$ . State each answer as an integer or an improper fraction in simplest form.
Answer Attempt 1 out of 2

Studdy Solution

STEP 1

What is this asking? We need to find the points where this line hits the x-axis and the y-axis! Watch out! Don't mix up the x and y intercepts!
Remember x-intercept means y is zero, and y-intercept means x is zero!

STEP 2

1. Find the x-intercept
2. Find the y-intercept

STEP 3

The x-intercept is where the line crosses the x-axis.
This happens when $y = 0$ !

STEP 4

Let's substitute $y = 0$ into our equation $3x - y = 37$ .
This gives us $3x - 0 = 37$ .

STEP 5

So, we have $3x = 37$ .
To isolate $x$ , we'll divide both sides by 3 (we're dividing to one to isolate $x$ ).
This gives us $x = \frac{37}{3}$ .
Boom!

STEP 6

Our x-intercept is $\left( \frac{37}{3}, 0 \right)$ .
Remember, the y-value is zero at the x-intercept!

STEP 7

The y-intercept is where the graph crosses the y-axis, which happens when $x = 0$ !

STEP 8

Now, we'll substitute $x = 0$ into our original equation $3x - y = 37$ .
This gives us $3 \cdot 0 - y = 37$ .

STEP 9

This simplifies to $-y = 37$ .
To get $y$ by itself, we'll multiply both sides by $-1$ .
This gives us $y = -37$ .
Awesome!

STEP 10

Our y-intercept is $(0, -37)$ .
Remember, the x-value is zero at the y-intercept!

STEP 11

The x-intercept is $\left( \frac{37}{3}, 0 \right)$ and the y-intercept is $(0, -37)$ .
We found where the line crosses both axes!

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QuestionQuestion Watch Video Show ExamplesFind the x - and y -intercepts of the graph of 3x−y=373 x-y=373x−y=37. State each answer as an integer or an improper fraction in simplest form.Answer Attempt 1 out of 2

Studdy Solution

STEP 1

What is this asking? We need to find the points where this line hits the x-axis and the y-axis! Watch out! Don't mix up the x and y intercepts!Remember x-intercept means y is **zero**, and y-intercept means x is **zero**!

STEP 2

1. Find the x-intercept2. Find the y-intercept

STEP 3

The x-intercept is where the line crosses the x-axis.This happens when y=0y = 0y=0!

STEP 4

Let's **substitute** y=0y = 0y=0 into our equation 3x−y=373x - y = 373x−y=37.This gives us 3x−0=373x - 0 = 373x−0=37.

STEP 5

So, we have 3x=373x = 373x=37.To **isolate** xxx, we'll **divide** both sides by **3** (we're dividing to one to isolate xxx).This gives us x=373x = \frac{37}{3}x=337​.Boom!

STEP 6

Our x-intercept is (373,0)\left( \frac{37}{3}, 0 \right)(337​,0).Remember, the y-value is **zero** at the x-intercept!

STEP 7

The y-intercept is where the graph crosses the y-axis, which happens when x=0x = 0x=0!

STEP 8

Now, we'll **substitute** x=0x = 0x=0 into our original equation 3x−y=373x - y = 373x−y=37.This gives us 3⋅0−y=373 \cdot 0 - y = 373⋅0−y=37.

STEP 9

This simplifies to −y=37-y = 37−y=37.To get yyy by itself, we'll **multiply** both sides by −1-1−1.This gives us y=−37y = -37y=−37.Awesome!

STEP 10

Our y-intercept is (0,−37)(0, -37)(0,−37).Remember, the x-value is **zero** at the y-intercept!

STEP 11

The x-intercept is (373,0)\left( \frac{37}{3}, 0 \right)(337​,0) and the y-intercept is (0,−37)(0, -37)(0,−37).We found where the line crosses both axes!

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QuestionQuestion Watch Video Show Examples
Find the x - and y -intercepts of the graph of $3 x-y=37$ . State each answer as an integer or an improper fraction in simplest form.
Answer Attempt 1 out of 2

What is this asking? We need to find the points where this line hits the x-axis and the y-axis! Watch out! Don't mix up the x and y intercepts!
Remember x-intercept means y is zero, and y-intercept means x is zero!

1. Find the x-intercept
2. Find the y-intercept

The x-intercept is where the line crosses the x-axis.
This happens when $y = 0$ !

Let's substitute $y = 0$ into our equation $3x - y = 37$ .
This gives us $3x - 0 = 37$ .

So, we have $3x = 37$ .
To isolate $x$ , we'll divide both sides by 3 (we're dividing to one to isolate $x$ ).
This gives us $x = \frac{37}{3}$ .
Boom!

Our x-intercept is $\left( \frac{37}{3}, 0 \right)$ .
Remember, the y-value is zero at the x-intercept!

The y-intercept is where the graph crosses the y-axis, which happens when $x = 0$ !

Now, we'll substitute $x = 0$ into our original equation $3x - y = 37$ .
This gives us $3 \cdot 0 - y = 37$ .

This simplifies to $-y = 37$ .
To get $y$ by itself, we'll multiply both sides by $-1$ .
This gives us $y = -37$ .
Awesome!

Our y-intercept is $(0, -37)$ .
Remember, the x-value is zero at the y-intercept!

The x-intercept is $\left( \frac{37}{3}, 0 \right)$ and the y-intercept is $(0, -37)$ .
We found where the line crosses both axes!