Math  /  Algebra

Questionnd the yy-intercept and the slope of the line. y=114xy=-1-\frac{1}{4} x yy-intercept: \square
Undefined slope:

Studdy Solution

STEP 1

What is this asking? We're looking for where this line crosses the yy-axis (that's the yy-intercept) and how steep it is (that's the slope). Watch out! Don't mix up the slope and the yy-intercept!
The yy-intercept is a *point*, and the slope is a *number* that tells us how slanted the line is.

STEP 2

1. Rewrite the equation
2. Identify the yy-intercept
3. Identify the slope

STEP 3

Let's **rewrite** our equation y=114xy = -1 - \frac{1}{4}x in the **slope-intercept form**, which is y=mx+by = mx + b.
This form makes it super easy to spot the slope and the yy-intercept.
Remember, mm is the **slope** and bb is the yy-intercept.

STEP 4

Rewriting the given equation, we get y=14x1y = -\frac{1}{4}x - 1.
See how we just swapped the order of the terms?
Now it looks just like y=mx+by = mx + b!

STEP 5

Now, let's **find** that yy-intercept!
In the equation y=mx+by = mx + b, the yy-intercept is bb, which is the **constant term**.
In our rewritten equation, y=14x1y = -\frac{1}{4}x - 1, the constant term is 1-1.

STEP 6

So, our yy-intercept is 1-1.
This means the line crosses the yy-axis at the point (0,1)(0, -1).
Remember, the xx-coordinate is always zero at the yy-intercept!

STEP 7

Time to **find** the slope!
In the equation y=mx+by = mx + b, the slope is represented by mm, which is the **coefficient** of xx.
Looking at our rewritten equation, y=14x1y = -\frac{1}{4}x - 1, we can see that the coefficient of xx is 14-\frac{1}{4}.

STEP 8

Therefore, our slope is 14-\frac{1}{4}.
This tells us that for every **1 unit** we move to the right along the xx-axis, we move **down** 14\frac{1}{4} units along the yy-axis.
The negative sign means the line goes downhill from left to right!

STEP 9

yy-intercept: 1-1 Slope: 14-\frac{1}{4}

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