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Math  /  Algebra

QuestionGraph the line with the equation y=−13x−5y = -\frac{1}{3}x - 5.

Studdy Solution

STEP 1

What is this asking? Draw the line represented by the equation y=−13x−5y = -\frac{1}{3}x - 5. Watch out! Don't mix up the **slope** and the **y-intercept**.

STEP 2

1. Identify Slope and Y-intercept
2. Plot the Y-intercept
3. Use the Slope to Find a Second Point
4. Draw the Line

STEP 3

The equation is in **slope-intercept form**, y=mx+by = mx + b, where mm is the **slope** and bb is the **y-intercept**.

STEP 4

In our equation, y=−13x−5y = -\frac{1}{3}x - 5, the **slope** mm is −13-\frac{1}{3} and the **y-intercept** bb is −5-5.
This means for every **3** units we move to the right along the x-axis, we move **1** unit *down* along the y-axis.

STEP 5

The **y-intercept** is where the line crosses the y-axis.
Since our **y-intercept** is −5-5, we plot a point at (0,−5)(0, -5).

STEP 6

Starting from our **y-intercept** (0,−5)(0, -5), we use the **slope** to find another point.

STEP 7

Our **slope** is −13-\frac{1}{3}.
This tells us that for every **3** units we increase xx, we decrease yy by **1** unit.

STEP 8

So, starting at (0,−5)(0, -5), we move **3** units to the right (xx increases by 3) and **1** unit down (yy decreases by 1).
This gives us the point (0+3,−5−1)=(3,−6)(0 + 3, -5 - 1) = (3, -6).

STEP 9

We have two points: (0,−5)(0, -5) and (3,−6)(3, -6).
Now, we simply draw a straight line through these two points, extending it in both directions.

STEP 10

The line is drawn through the points (0,−5)(0, -5) and (3,−6)(3, -6) and extends infinitely in both directions.

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