Math / Algebra

QuestionXLL Graph a line from an equ |x| com-math/grade-8/graph-a-line-from-an-equation-in-standard-form
Graph this line using intercepts: $7 x+y=-7$ Click to select points on the graph.

Studdy Solution

STEP 1

What is this asking? We need to draw a line on a graph, and the line is described by the equation $7x + y = -7$ .
We're going to do this the smart way, using intercepts! Watch out! Make sure you calculate the intercepts correctly, and don't mix up the x and y values!
Also, remember that an intercept is where the line crosses an axis!

STEP 2

1. Find the x-intercept
2. Find the y-intercept
3. Draw the line

STEP 3

The x-intercept is where our line crosses the x-axis.
What's special about the x-axis?
The y-value is always zero!

STEP 4

So, to find the x-intercept, we take our equation, $7x + y = -7$ , and plug in $y = 0$ .
This gives us $7x + 0 = -7$ .

STEP 5

Now, we just need to solve for $x$ !
We have $7x = -7$ .
We can divide both sides by 7 to get $x$ by itself.
So, $\frac{7x}{7} = \frac{-7}{7}$ , which simplifies to $x = -1$ .
Boom!

STEP 6

Our x-intercept is $(-1, 0)$ .
That's one point on our line!

STEP 7

The y-intercept is where the line crosses the y-axis.
On the y-axis, the x-value is always zero!

STEP 8

We'll plug $x = 0$ into our equation: $7x + y = -7$ becomes $7 \cdot 0 + y = -7$ .

STEP 9

This simplifies to $0 + y = -7$ , which means $y = -7$ .
Awesome!

STEP 10

Our y-intercept is $(0, -7)$ .
That's another point on our line!

STEP 11

We have two points: the x-intercept at $(-1, 0)$ and the y-intercept at $(0, -7)$ .
Plot these points on your graph!

STEP 12

Now, take your ruler (or a straight edge) and draw a line straight through those two points.
Extend the line beyond the points in both directions.
Ta-da! You've graphed the line!

STEP 13

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

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QuestionXLL Graph a line from an equ |x| com-math/grade-8/graph-a-line-from-an-equation-in-standard-form
Graph this line using intercepts: $7 x+y=-7$ Click to select points on the graph.

Studdy Solution

STEP 1

STEP 2

1. Find the x-intercept
2. Find the y-intercept
3. Draw the line

STEP 3

The x-intercept is where our line crosses the x-axis.
What's special about the x-axis?
The y-value is always zero!

STEP 4

So, to find the x-intercept, we take our equation, $7x + y = -7$ , and plug in $y = 0$ .
This gives us $7x + 0 = -7$ .

STEP 5

Now, we just need to solve for $x$ !
We have $7x = -7$ .
We can divide both sides by 7 to get $x$ by itself.
So, $\frac{7x}{7} = \frac{-7}{7}$ , which simplifies to $x = -1$ .
Boom!

STEP 6

Our x-intercept is $(-1, 0)$ .
That's one point on our line!

STEP 7

The y-intercept is where the line crosses the y-axis.
On the y-axis, the x-value is always zero!

STEP 8

We'll plug $x = 0$ into our equation: $7x + y = -7$ becomes $7 \cdot 0 + y = -7$ .

STEP 9

This simplifies to $0 + y = -7$ , which means $y = -7$ .
Awesome!

STEP 10

Our y-intercept is $(0, -7)$ .
That's another point on our line!

STEP 11

We have two points: the x-intercept at $(-1, 0)$ and the y-intercept at $(0, -7)$ .
Plot these points on your graph!

STEP 12

Now, take your ruler (or a straight edge) and draw a line straight through those two points.
Extend the line beyond the points in both directions.
Ta-da! You've graphed the line!

STEP 13

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

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QuestionXLL Graph a line from an equ |x| com-math/grade-8/graph-a-line-from-an-equation-in-standard-formGraph this line using intercepts: 7x+y=−77 x+y=-77x+y=−7 Click to select points on the graph.

Studdy Solution

STEP 1

STEP 2

1. Find the x-intercept2. Find the y-intercept3. Draw the line

STEP 3

The **x-intercept** is where our line crosses the **x-axis**.What's special about the x-axis?The y-value is always **zero**!

STEP 4

So, to find the x-intercept, we take our equation, 7x+y=−77x + y = -77x+y=−7, and plug in y=0y = 0y=0.This gives us 7x+0=−77x + 0 = -77x+0=−7.

STEP 5

Now, we just need to solve for xxx!We have 7x=−77x = -77x=−7.We can divide both sides by **7** to get xxx by itself.So, 7x7=−77\frac{7x}{7} = \frac{-7}{7}77x​=7−7​, which simplifies to x=−1x = -1x=−1.Boom!

STEP 6

Our x-intercept is (−1,0)(-1, 0)(−1,0).That's one point on our line!

STEP 7

The **y-intercept** is where the line crosses the **y-axis**.On the y-axis, the x-value is always **zero**!

STEP 8

We'll plug x=0x = 0x=0 into our equation: 7x+y=−77x + y = -77x+y=−7 becomes 7⋅0+y=−77 \cdot 0 + y = -77⋅0+y=−7.

STEP 9

This simplifies to 0+y=−70 + y = -70+y=−7, which means y=−7y = -7y=−7.Awesome!

STEP 10

Our y-intercept is (0,−7)(0, -7)(0,−7).That's another point on our line!

STEP 11

We have two points: the x-intercept at (−1,0)(-1, 0)(−1,0) and the y-intercept at (0,−7)(0, -7)(0,−7).Plot these points on your graph!

STEP 12

Now, take your ruler (or a straight edge) and draw a line straight through those two points.Extend the line beyond the points in both directions.Ta-da! You've graphed the line!

STEP 13

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

Get Studdy

Studdy solves anything!

Start learning now

Download Studdy AI Tutor now. Learn with ease and get all help you need to be successful at school.

QuestionXLL Graph a line from an equ |x| com-math/grade-8/graph-a-line-from-an-equation-in-standard-form
Graph this line using intercepts: $7 x+y=-7$ Click to select points on the graph.

1. Find the x-intercept
2. Find the y-intercept
3. Draw the line

The x-intercept is where our line crosses the x-axis.
What's special about the x-axis?
The y-value is always zero!

So, to find the x-intercept, we take our equation, $7x + y = -7$ , and plug in $y = 0$ .
This gives us $7x + 0 = -7$ .

Now, we just need to solve for $x$ !
We have $7x = -7$ .
We can divide both sides by 7 to get $x$ by itself.
So, $\frac{7x}{7} = \frac{-7}{7}$ , which simplifies to $x = -1$ .
Boom!

Our x-intercept is $(-1, 0)$ .
That's one point on our line!

The y-intercept is where the line crosses the y-axis.
On the y-axis, the x-value is always zero!

We'll plug $x = 0$ into our equation: $7x + y = -7$ becomes $7 \cdot 0 + y = -7$ .

This simplifies to $0 + y = -7$ , which means $y = -7$ .
Awesome!

Our y-intercept is $(0, -7)$ .
That's another point on our line!

We have two points: the x-intercept at $(-1, 0)$ and the y-intercept at $(0, -7)$ .
Plot these points on your graph!

Now, take your ruler (or a straight edge) and draw a line straight through those two points.
Extend the line beyond the points in both directions.
Ta-da! You've graphed the line!

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