Math / Algebra

QuestionGraph this line using intercepts: $7x - y = -7$ Click to select points on the graph.

Studdy Solution

STEP 1

What is this asking? We need to draw a line on the graph by finding where it crosses the $\text{x}$ and $\text{y}$ axes. Watch out! Don't mix up the $\text{x}$ and $\text{y}$ intercepts!
Also, remember that intercepts are where the line crosses the axes, not just any point on the line.

STEP 2

1. Find the x-intercept
2. Find the y-intercept
3. Plot the intercepts and draw the line

STEP 3

To find the $\text{x}$ -intercept, we set $\text{y}$ equal to zero in our equation, because the $\text{x}$ -intercept is where the line crosses the $\text{x}$ -axis, and the $\text{y}$ -value is always zero there.
Think of it like this: the $\text{x}$ -axis is just a horizontal line where $\text{y}$ is always zero!

STEP 4

So, we substitute $\text{y} = 0$ into our equation $7\text{x} - \text{y} = -7$ : $7\text{x} - 0 = -7$ $7\text{x} = -7$

STEP 5

Now, we want to isolate $\text{x}$ , so we divide both sides of the equation by 7.
Remember, what we do to one side, we must do to the other to keep things balanced! $\frac{7\text{x}}{7} = \frac{-7}{7}$ $\text{x} = -1$ So, our $\text{x}$ -intercept is $(-1, 0)$ !

STEP 6

Now, let's find the $\text{y}$ -intercept!
Similar to before, the $\text{y}$ -intercept is where the line crosses the $\text{y}$ -axis, and the $\text{x}$ -value is always zero there.
The $\text{y}$ -axis is just a vertical line where $\text{x}$ is always zero!

STEP 7

We substitute $\text{x} = 0$ into our equation $7\text{x} - \text{y} = -7$ : $7 \cdot 0 - \text{y} = -7$ $0 - \text{y} = -7$ $-\text{y} = -7$

STEP 8

We want $\text{y}$ by itself, not $-\text{y}$ .
We can multiply both sides by $-1$ to get $\text{y}$ all alone: $(-1) \cdot (-\text{y}) = (-1) \cdot (-7)$ $\text{y} = 7$ So our $\text{y}$ -intercept is $(0, 7)$ !

STEP 9

We found our x-intercept is $(-1, 0)$ and our y-intercept is $(0, 7)$ .
Now, we plot these two points on the graph.

STEP 10

Finally, we draw a straight line through these two points, extending it beyond the points in both directions.
And there you have it, the line of the equation $7\text{x} - \text{y} = -7$ graphed using its intercepts!

STEP 11

The line passes through the points $(-1, 0)$ and $(0, 7)$ .

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QuestionGraph this line using intercepts: $7x - y = -7$ Click to select points on the graph.

Studdy Solution

STEP 1

What is this asking? We need to draw a line on the graph by finding where it crosses the $\text{x}$ and $\text{y}$ axes. Watch out! Don't mix up the $\text{x}$ and $\text{y}$ intercepts!
Also, remember that intercepts are where the line crosses the axes, not just any point on the line.

STEP 2

1. Find the x-intercept
2. Find the y-intercept
3. Plot the intercepts and draw the line

STEP 3

STEP 4

So, we substitute $\text{y} = 0$ into our equation $7\text{x} - \text{y} = -7$ : $7\text{x} - 0 = -7$ $7\text{x} = -7$

STEP 5

Now, we want to isolate $\text{x}$ , so we divide both sides of the equation by 7.
Remember, what we do to one side, we must do to the other to keep things balanced! $\frac{7\text{x}}{7} = \frac{-7}{7}$ $\text{x} = -1$ So, our $\text{x}$ -intercept is $(-1, 0)$ !

STEP 6

Now, let's find the $\text{y}$ -intercept!
Similar to before, the $\text{y}$ -intercept is where the line crosses the $\text{y}$ -axis, and the $\text{x}$ -value is always zero there.
The $\text{y}$ -axis is just a vertical line where $\text{x}$ is always zero!

STEP 7

We substitute $\text{x} = 0$ into our equation $7\text{x} - \text{y} = -7$ : $7 \cdot 0 - \text{y} = -7$ $0 - \text{y} = -7$ $-\text{y} = -7$

STEP 8

We want $\text{y}$ by itself, not $-\text{y}$ .
We can multiply both sides by $-1$ to get $\text{y}$ all alone: $(-1) \cdot (-\text{y}) = (-1) \cdot (-7)$ $\text{y} = 7$ So our $\text{y}$ -intercept is $(0, 7)$ !

STEP 9

We found our x-intercept is $(-1, 0)$ and our y-intercept is $(0, 7)$ .
Now, we plot these two points on the graph.

STEP 10

Finally, we draw a straight line through these two points, extending it beyond the points in both directions.
And there you have it, the line of the equation $7\text{x} - \text{y} = -7$ graphed using its intercepts!

STEP 11

The line passes through the points $(-1, 0)$ and $(0, 7)$ .

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QuestionGraph this line using intercepts: 7x−y=−77x - y = -77x−y=−7 Click to select points on the graph.

Studdy Solution

STEP 1

What is this asking? We need to draw a line on the graph by finding where it crosses the x\text{x}x and y\text{y}y axes. Watch out! Don't mix up the x\text{x}x and y\text{y}y intercepts!Also, remember that intercepts are where the line crosses the axes, not just any point on the line.

STEP 2

1. Find the x-intercept2. Find the y-intercept3. Plot the intercepts and draw the line

STEP 3

STEP 4

So, we substitute y=0\text{y} = 0y=0 into our equation 7x−y=−77\text{x} - \text{y} = -77x−y=−7: 7x−0=−77\text{x} - 0 = -77x−0=−7 7x=−77\text{x} = -77x=−7

STEP 5

STEP 6

Now, let's find the y\text{y}y-intercept!Similar to before, the y\text{y}y-intercept is where the line crosses the y\text{y}y-axis, and the x\text{x}x-value is always **zero** there.The y\text{y}y-axis is just a vertical line where x\text{x}x is always zero!

STEP 7

We substitute x=0\text{x} = 0x=0 into our equation 7x−y=−77\text{x} - \text{y} = -77x−y=−7: 7⋅0−y=−77 \cdot 0 - \text{y} = -77⋅0−y=−7 0−y=−70 - \text{y} = -70−y=−7−y=−7-\text{y} = -7−y=−7

STEP 8

We want y\text{y}y by itself, not −y-\text{y}−y.We can **multiply both sides** by −1-1−1 to get y\text{y}y all alone: (−1)⋅(−y)=(−1)⋅(−7)(-1) \cdot (-\text{y}) = (-1) \cdot (-7)(−1)⋅(−y)=(−1)⋅(−7) y=7\text{y} = 7y=7So our y\text{y}y-intercept is (0,7)(0, 7)(0,7)!

STEP 9

We found our **x-intercept** is (−1,0)(-1, 0)(−1,0) and our **y-intercept** is (0,7)(0, 7)(0,7).Now, we **plot these two points** on the graph.

STEP 10

Finally, we **draw a straight line** through these two points, extending it beyond the points in both directions.And there you have it, the line of the equation 7x−y=−77\text{x} - \text{y} = -77x−y=−7 graphed using its intercepts!

STEP 11

The line passes through the points (−1,0)(-1, 0)(−1,0) and (0,7)(0, 7)(0,7).

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QuestionGraph this line using intercepts: $7x - y = -7$ Click to select points on the graph.

What is this asking? We need to draw a line on the graph by finding where it crosses the $\text{x}$ and $\text{y}$ axes. Watch out! Don't mix up the $\text{x}$ and $\text{y}$ intercepts!
Also, remember that intercepts are where the line crosses the axes, not just any point on the line.

1. Find the x-intercept
2. Find the y-intercept
3. Plot the intercepts and draw the line

So, we substitute $\text{y} = 0$ into our equation $7\text{x} - \text{y} = -7$ : $7\text{x} - 0 = -7$ $7\text{x} = -7$

Now, let's find the $\text{y}$ -intercept!
Similar to before, the $\text{y}$ -intercept is where the line crosses the $\text{y}$ -axis, and the $\text{x}$ -value is always zero there.
The $\text{y}$ -axis is just a vertical line where $\text{x}$ is always zero!

We substitute $\text{x} = 0$ into our equation $7\text{x} - \text{y} = -7$ : $7 \cdot 0 - \text{y} = -7$ $0 - \text{y} = -7$ $-\text{y} = -7$

We want $\text{y}$ by itself, not $-\text{y}$ .
We can multiply both sides by $-1$ to get $\text{y}$ all alone: $(-1) \cdot (-\text{y}) = (-1) \cdot (-7)$ $\text{y} = 7$ So our $\text{y}$ -intercept is $(0, 7)$ !

We found our x-intercept is $(-1, 0)$ and our y-intercept is $(0, 7)$ .
Now, we plot these two points on the graph.

Finally, we draw a straight line through these two points, extending it beyond the points in both directions.
And there you have it, the line of the equation $7\text{x} - \text{y} = -7$ graphed using its intercepts!

The line passes through the points $(-1, 0)$ and $(0, 7)$ .