1. The problem states that the line $T$ passes through the points $(0, -5)$ and $(1, 3)$ and can be written in the form $y = mx + c$. 2. To find $m$ (the slope), use the formula: $$m = \frac{y_2 - y_1}{x_2 - x_1}$$ where $(x_1, y_1) = (0, -5)$ and $(x_2, y_2) = (1, 3)$. 3. Substitute the values: $$m = \frac{3 - (-5)}{1 - 0} = \frac{3 + 5}{1} = \frac{8}{1} = 8$$ 4. To find $c$ (the y-intercept), use the point where $x=0$. From the point $(0, -5)$, we see directly that: $$c = -5$$ 5. Therefore, the equation of the line $T$ is: $$y = 8x - 5$$ 6. Summary: - Slope $m = 8$ - Y-intercept $c = -5$