To find the equation of the linear function represented by the table in slope-intercept form, we need to calculate the slope ($m$) and y-intercept ($b$) of the line.

The table provides these pairs of $(x, y)$ values:

• $(-4, -21)$
• $(1, -1)$
• $(6, 19)$
• $(11, 39)$

Step 1: Calculate the Slope ($m$)

The slope $m$ is found using the formula: $m = \frac{y_2 - y_1}{x_2 - x_1}$

Let's use the points $(1, -1)$ and $(6, 19)$ from the table: $m = \frac{19 - (-1)}{6 - 1} = \frac{19 + 1}{5} = \frac{20}{5} = 4$

So, the slope $m = 4$.

Step 2: Find the y-Intercept ($b$)

With the slope $m = 4$, we can use the slope-intercept form $y = mx + b$ with one of the points to solve for $b$.

Using the point $(1, -1)$: $-1 = 4(1) + b$ $-1 = 4 + b$ $b = -1 - 4 = -5$

Conclusion

The equation of the line in slope-intercept form is: $y = 4x - 5$

Would you like more details, or do you have any questions?

Further Practice Questions

1. Verify the equation $y = 4x - 5$ with the other points in the table.
2. Find the slope-intercept form if the points were $(-2, -13)$ and $(2, 5)$.
3. Convert $y = 4x - 5$ to standard form $Ax + By = C$.
4. Determine the y-intercept of a line with slope $-3$ passing through $(0, 4)$.
5. Calculate the slope of a line passing through $(5, 10)$ and $(10, 25)$.

Tip

When finding the equation of a line from a table, always start by calculating the slope using any two points. This will help you check if the relationship is indeed linear.