To solve for the slope and y-intercept of the given linear function based on the graph, we will follow these steps:

1. Finding the slope:

The formula for the slope between two points $(x_1, y_1)$ and $(x_2, y_2)$ is: $m = \frac{y_2 - y_1}{x_2 - x_1}$

Using the given points $(-4, -3)$ and $(4, -1)$: $m = \frac{-1 - (-3)}{4 - (-4)} = \frac{-1 + 3}{4 + 4} = \frac{2}{8} = \frac{1}{4}$

Thus, the slope $m = \frac{1}{4}$.

2. Finding the y-intercept:

The y-intercept occurs when $x = 0$. Using the slope-intercept form $y = mx + b$, where $b$ is the y-intercept, we can substitute one of the points and the slope to solve for $b$.

Using point $(4, -1)$ and $m = \frac{1}{4}$: $-1 = \frac{1}{4}(4) + b$ $-1 = 1 + b$ $b = -1 - 1 = -2$

Thus, the y-intercept is $(0, -2)$.

Final answers:

• Slope: $\frac{1}{4}$
• y-intercept: $(0, -2)$

Would you like more details or have any questions?

Related questions:

1. How do you calculate the slope when the coordinates involve negative values?
2. How do you find the equation of a line given two points?
3. What are some alternative ways to determine the y-intercept from a graph?
4. How would you graph a line if you only knew the slope and y-intercept?
5. How does changing the slope affect the steepness of a line?

Tip:

When finding the slope between two points, be careful with signs—subtracting a negative value is the same as adding its positive counterpart.