Lillian graphed a linear function through the points (‒7, ‒4) and (7, 6). What are the slope and y-intercept of the graph?
 

A.The slope is 57
 , and the y-intercept is ‒1.
B.The slope is 57
 , and the y-intercept is 1.
C.The slope is 75
 , and the y-intercept is ‒1.
D.The slope is 75
 , and the y-intercept is ‒1.


To solve for the slope and y-intercept of the linear function passing through the points \((-7, -4)\) and \( (7, 6)\), let's follow these steps:

### Step 1: Find the Slope
The formula for the slope \(m\) of a line passing through two points \((x_1, y_1)\) and \((x_2, y_2)\) is:

\[
m = \frac{y_2 - y_1}{x_2 - x_1}
\]

Substituting the given points \((-7, -4)\) and \( (7, 6)\):

\[
m = \frac{6 - (-4)}{7 - (-7)} = \frac{6 + 4}{7 + 7} = \frac{10}{14} = \frac{5}{7}
\]

So, the slope \(m\) is \( \frac{5}{7} \).

### Step 2: Find the Y-intercept
The equation of a line in slope-intercept form is:

\[
y = mx + b
\]

Where \(m\) is the slope and \(b\) is the y-intercept. We can use one of the points and the slope to solve for \(b\).

Using the point \((-7, -4)\):

\[
-4 = \frac{5}{7}(-7) + b
\]

Simplify and solve for \(b\):

\[
-4 = -5 + b \implies b = -4 + 5 = 1
\]

So, the y-intercept \(b\) is \(1\).

### Conclusion
The correct answer is:
**B. The slope is \(\frac{5}{7}\), and the y-intercept is 1.**

Would you like further details or have any questions?

Here are 5 related questions:
1. How would you find the equation of the line given a different set of points?
2. Can you explain why the slope formula works?
3. How do you convert between different forms of a linear equation?
4. What does the slope represent in a real-world context?
5. How can you graph a line using its slope and y-intercept?

**Tip:** Remember that the y-intercept is where the line crosses the y-axis, which means \(x = 0\) at that point.

Lillian graphed a linear function through the points (‒7, ‒4) and (7, 6). What are the slope and y-intercept of the graph?

A. The slope is 5/7, and the y-intercept is ‒1.
B. The slope is 5/7, and the y-intercept is 1.
C. The slope is 7/5, and the y-intercept is ‒1.
D. The slope is 7/5, and the y-intercept is ‒1.

Learn how to find the slope and y-intercept of a linear function that passes through the points (‒7, ‒4) and (7, 6). This problem involves using the slope formula and understanding the slope-intercept form of a line. Suitable for students in Grades 8-10.

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