1. **State the problem:** Find the equation of the straight line passing through the points $(-5,0)$ and $(0,7)$ in the form $y = mx + c$. 2. **Formula used:** The equation of a line is $y = mx + c$, where $m$ is the slope and $c$ is the y-intercept. 3. **Calculate the slope $m$:** $$m = \frac{y_2 - y_1}{x_2 - x_1} = \frac{7 - 0}{0 - (-5)} = \frac{7}{5}$$ 4. **Find the y-intercept $c$:** Since the line passes through $(0,7)$, the y-intercept is $c = 7$. 5. **Write the equation:** $$y = \frac{7}{5}x + 7$$ This is the equation of the line passing through the given points.