Math  /  Algebra

QuestionA line has a slope of 0 and passes through the point (7,19)(7,19). Write its equation in slopeintercept form.
Write your answer using integers, proper fractions, and improper fractions in simplest form \square

Studdy Solution

STEP 1

What is this asking? We need to find the equation of a line that is flat (because its slope is **zero**) and goes through the point (7,197, 19). Watch out! A slope of zero doesn't mean there's no line!
It just means the line is perfectly horizontal.

STEP 2

1. Understand Slope-Intercept Form
2. Plug in the Slope
3. Find the y-intercept
4. Write the Final Equation

STEP 3

Let's remember what slope-intercept form looks like: y=mx+by = mx + b.
Here, mm is the **slope** of the line, and bb is the **y-intercept** (where the line crosses the y-axis).

STEP 4

We know the slope is **zero**, so we can plug that into our equation: y=0x+by = 0 \cdot x + b.

STEP 5

Simplifying, we get y=by = b.
See how the *x* term disappears when the slope is zero?
This is why horizontal lines have equations like *y = some number*.

STEP 6

We know the line passes through the point (7,197, 19).
This means when x=7x = 7, y=19y = 19.

STEP 7

Let's plug these values into our simplified equation: 19=b19 = b.
Boom! We found our y-intercept: it's **19**!

STEP 8

Now, we just put it all together.
We know y=by = b, and we found that b=19b = 19.

STEP 9

So, the equation of our line is y=19y = 19!

STEP 10

y=19y = 19

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