The image shows a math problem that involves graphing inequalities. The inequalities provided are:

1. $y \geq -5x + 3$
2. $y > -2$

These inequalities need to be graphed on a coordinate plane. Here's how you would approach graphing each one:

1. Graphing $y \geq -5x + 3$:

• Slope-Intercept Form: The inequality is in the form $y \geq mx + b$ where $m = -5$ (slope) and $b = 3$ (y-intercept).
• Plot the Line: Start by plotting the y-intercept at $(0, 3)$. From there, use the slope $-5$ to find another point on the line. For every 1 unit you move to the right (positive direction on the x-axis), you move down 5 units (negative direction on the y-axis).
• Line Type: Since the inequality is $\geq$, the line should be solid, indicating that points on the line are included in the solution.
• Shading: Shade above the line because $y$ is greater than or equal to the expression.

2. Graphing $y > -2$:

• Horizontal Line: This inequality represents a horizontal line where $y = -2$.
• Line Type: Since the inequality is strictly greater than ( $y > -2$ ), the line should be dashed to indicate that points on the line are not included in the solution.
• Shading: Shade above the line because $y$ is greater than $-2$.

Intersection:

• The solution to the system of inequalities is the region where the shading of both inequalities overlaps. This represents all the points that satisfy both inequalities simultaneously.

If you were to plot this on a graph, you'd see a region that is above both the solid line $y = -5x + 3$ and the dashed line $y = -2$.

Would you like a detailed step-by-step guide on how to solve similar problems, or do you have any questions about this problem?

Related Questions:

1. How do you determine whether to use a solid or dashed line when graphing inequalities?
2. What is the importance of shading in graphing inequalities?
3. How does the slope of a line affect its steepness and direction on a graph?
4. What methods can you use to check if a point lies within the solution region of a system of inequalities?
5. How would the graph change if the inequality was $y \leq -5x + 3$ instead of $y \geq -5x + 3$?

Tip:

When graphing systems of inequalities, always ensure that you accurately differentiate between solid and dashed lines, as well as the direction of shading, to correctly represent the solution region.