To find the equation of the straight line shown in the form $y = mx + c$, where $m$ is the slope and $c$ is the y-intercept, let’s analyze the graph provided:

1. Determine the Slope ($m$):

   • The slope, $m$, is calculated by finding two points on the line and using the formula $m = \frac{\Delta y}{\Delta x}$.
   • From the graph, two clear points on the line are:
     • Point A: $(0, 5)$
     • Point B: $(3, 0)$
   • Calculating the slope: $m = \frac{0 - 5}{3 - 0} = \frac{-5}{3}$
   • Therefore, the slope $m = -\frac{5}{3}$.

2. Determine the Y-Intercept ($c$):

   • The y-intercept is the point where the line crosses the y-axis.
   • Observing the graph, the line crosses the y-axis at $y = 5$, so $c = 5$.

3. Form the Equation:

   • With $m = -\frac{5}{3}$ and $c = 5$, the equation of the line is: $y = -\frac{5}{3}x + 5$

Final Answer

The equation of the line is: $y = -\frac{5}{3}x + 5$

Would you like more details or have any questions?

Here are some related questions to deepen your understanding:

1. How do you calculate the slope if only one point and the y-intercept are known?
2. Can you explain how changing the slope affects the steepness of the line?
3. What would the equation be if the line had a positive slope instead?
4. How can you determine the x-intercept from the line equation?
5. What does it mean graphically if $c$, the y-intercept, is zero?

Tip: The slope tells you the direction and steepness of a line—negative slopes descend from left to right, while positive slopes ascend.