To graph the system of inequalities y = -5x + 3, follow these steps:
1. Define the line: The equation y = -5x + 3 is a linear equation. It can be graphed by identifying the y-intercept and the slope.
2. Find the y-intercept: The equation is in the form y = mx + b, where m is the slope and b is the y-intercept. With the equation y = -5x + 3, the y-intercept is at b = 3. This implies that the line crosses the y-axis at the point (0, 3).
3. Determine the slope: In the equation y = -5x + 3, the slope, m, is -5. Slope is the ratio of vertical change (change in y) to horizontal change (change in x). A slope of -5 means that for every 1 unit increase in x, y decreases by 5 units.
4. Draw the line: Start from the y-intercept (0, 3). As the slope is -5, from the y-intercept, you move down 5 units and to the right 1 unit to find another point on the line. Keep doing this until you have enough points to draw the line.
5. Shading the graph: Since the question says y ≤ -5x + 3, all solutions to the inequality are either on the line or are below it. This is because the inequality symbol is '≤', which means 'less than or equal to'. Hence, shade all of the area below the line to demonstrate that any point in that region is a solution to the inequality.
Now the graph is ready, and you can see the solutions to the inequality system. This line and the shaded region represent all possible solutions to the inequality y ≤ -5x + 3. This implies that for any point in the shaded region, if you substitute the x and y values of that point into the inequality, it will make the inequality true.