Silas claims that the equation y = 2 + mx, where m is a real number, represents a function whose graph is a straight line

To determine whether the equation y = 2 + mx represents a function with a straight line graph, we need to analyze its properties.

1. Form of the equation: The equation y = 2 + mx is in slope-intercept form, which represents a linear function with a constant slope (m) and a y-intercept of 2.

2. Coefficients: The coefficient of x is m, which can be any real number. This means that the slope of the line can take on any real value.

3. Graph shape: Since the equation is linear and has a constant slope, the graph will be a straight line.

4. y-intercept: The y-intercept of the line is 2, meaning that the line crosses the y-axis at the point (0, 2).

Based on these properties, it can be concluded that the equation y = 2 + mx represents a function whose graph is a straight line.

To determine if the equation y = 2 + mx represents a function whose graph is a straight line, we need to verify if it satisfies the criteria for a linear function.

In a linear equation, the dependent variable (y) is directly proportional to an independent variable (x) multiplied by a constant (m) and added to another constant (2 in this case). This equation is in the slope-intercept form, y = mx + b, where b represents the y-intercept.

To establish that the equation represents a straight line, we need to confirm if it meets the following conditions:

1. Every x-value corresponds to only one y-value: For any given value of x, plugging it into the equation will result in a unique value for y. In this case, each x-value will produce one corresponding y-value.

2. The graph is a straight line: If the equation is linear, the graph will appear as a straight line on a coordinate plane. To verify this, we can plot a few points on the graph.

For example, let's assume m = 2. We can select different x-values and calculate the corresponding y-values:

When x = 0: y = 2 + (2 * 0) = 2
When x = 1: y = 2 + (2 * 1) = 4
When x = -1: y = 2 + (2 * -1) = 0

Plotting these points on a graph will show that they lie in a straight line. If we repeat this process for any real value of m, the graph will remain a straight line.

Therefore, based on the criteria for a linear function and the confirmation through plotting, we can conclude that the equation y = 2 + mx, where m is a real number, represents a function whose graph is a straight line.

Silas has a valid claim