Find the vertical intercept and slope of the line:  7x-4y=19   a. The y-coordinate of the vertical temperature.   b. The slope:

We are given the equation of a line: 

\[
7x - 4y = 19
\]

To find the **y-intercept** and **slope**, we first rewrite the equation in slope-intercept form \((y = mx + b)\), where \(m\) is the slope and \(b\) is the y-intercept.

### Step 1: Rewrite the equation in slope-intercept form.
We want to solve for \(y\):

\[
7x - 4y = 19
\]

Subtract \(7x\) from both sides:

\[
-4y = -7x + 19
\]

Now, divide everything by \(-4\) to isolate \(y\):

\[
y = \frac{-7x + 19}{-4}
\]

Simplify:

\[
y = \frac{7}{4}x - \frac{19}{4}
\]

Now we have the equation in slope-intercept form:

\[
y = \frac{7}{4}x - \frac{19}{4}
\]

### Step 2: Identify the slope and y-intercept.

From the equation \(y = \frac{7}{4}x - \frac{19}{4}\):

- The **slope** \(m\) is \(\frac{7}{4}\).
- The **y-intercept** is \(-\frac{19}{4}\), meaning the **y-coordinate of the intercept** is \(-\frac{19}{4}\).

### Final Answer:
a. The **y-coordinate of the vertical intercept**: \(-\frac{19}{4}\)  
b. The **slope**: \(\frac{7}{4}\)

Would you like more details or have any questions?

### Related Questions:
1. How do you find the x-intercept of the line \(7x - 4y = 19\)?
2. What is the significance of the slope in interpreting a line?
3. How can you verify the slope by plotting the line?
4. How does the y-intercept affect the graph of the line?
5. What happens to the slope if the equation of the line changes to \(7x + 4y = 19\)?

**Tip:** Always convert equations to slope-intercept form when identifying slope and intercepts for simplicity!

Find the vertical intercept and slope of the line: 7x-4y=19. a. The y-coordinate of the vertical intercept. b. The slope:

Discover how to calculate the slope and y-intercept of the linear equation 7x - 4y = 19. This problem explores key algebraic concepts like linear equations, slope-intercept form, and the Slope-Intercept Theorem, making it suitable for students in Grades 8-10.

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