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Math  /  Algebra

QuestionGraph the line with the equation y=−25x+1y = -\frac{2}{5}x + 1.

Studdy Solution

STEP 1

What is this asking? Draw the line represented by the equation y=−25x+1y = -\frac{2}{5}x + 1 on the coordinate plane. Watch out! Don't mix up the **slope** and the **y-intercept**!

STEP 2

1. Identify the y-intercept.
2. Identify the slope.
3. Plot the y-intercept.
4. Use the slope to find a second point.
5. Draw the line.

STEP 3

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

STEP 4

In our equation, y=−25x+1y = -\frac{2}{5}x + 1, the **y-intercept** is b=1b = \mathbf{1}.
This tells us that the line crosses the y-axis at the point (0,1)(0, 1).

STEP 5

In our equation, y=−25x+1y = -\frac{2}{5}x + 1, the **slope** is m=−25m = \mathbf{-\frac{2}{5}}.

STEP 6

Remember, the slope is the "rise over run".
A **negative slope** means the line goes *down* as we move from left to right.

STEP 7

We found that the **y-intercept** is 1\mathbf{1}, so we plot the point (0,1)(0, 1) on the graph.
This is our **starting point**.

STEP 8

Our **slope** is −25-\frac{2}{5}.
This means for every **5** units we move to the *right* along the x-axis (the **run**), we move **2** units *down* along the y-axis (the **rise**).

STEP 9

Starting from our **y-intercept** (0,1)(0, 1), we move **5** units to the right, which takes us to x=5x = 5.

STEP 10

Then, we move **2** units *down* from y=1y = 1, which takes us to y=1−2=−1y = 1 - 2 = -1.

STEP 11

So, our second point is (5,−1)(5, -1).

STEP 12

Now that we have two points, (0,1)(0, 1) and (5,−1)(5, -1), we can draw a straight line through them.
Make sure your line extends to the edges of the graph!

STEP 13

The line passing through the points (0,1)(0, 1) and (5,−1)(5, -1) represents the graph of the equation y=−25x+1y = -\frac{2}{5}x + 1.

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