To determine the values of $m$ (the slope) and $c$ (the y-intercept) for line $T$ from the graph, follow these steps:

1. Identify Two Points on the Line

Choose two points through which the line passes to calculate the slope. From the graph, it looks like line $T$ passes through these points:

• Point 1: $(-4, -1)$
• Point 2: $(0, 3)$

2. Calculate the Slope $m$

The slope $m$ of a line through two points $(x_1, y_1)$ and $(x_2, y_2)$ is calculated as: $m = \frac{y_2 - y_1}{x_2 - x_1}$ Substitute the points: $m = \frac{3 - (-1)}{0 - (-4)} = \frac{3 + 1}{4} = \frac{4}{4} = 1$ So, $m = 1$.

3. Find the Y-Intercept $c$

The y-intercept $c$ is the y-coordinate when $x = 0$. From Point 2, we see that $(0, 3)$ is on the line, meaning: $c = 3$

Conclusion

The equation of line $T$ is: $y = x + 3$ where:

• $m = 1$
• $c = 3$

Would you like more details or have any questions?

Related Questions

1. How do you find the equation of a line given two points?
2. What does the slope represent in the context of a line?
3. How can you convert an equation in standard form to slope-intercept form?
4. What happens to the graph of a line if the slope $m$ is negative?
5. How does the y-intercept $c$ affect where the line crosses the y-axis?

Tip

To find the slope between two points accurately, always ensure they are clear intersections on the graph for precision.