1. The problem is to understand how the value of $m$ in linear equations of type $y = mx + c$ affects the graph. 2. We have two linear functions given: (a) $f(x) = x + 1$ which means here $m=1$ and $c=1$. (b) $f(x) = 2x + 1$ which means here $m=2$ and $c=1$. 3. Both functions have the same intercept $c = 1$, but different slopes $m = 1$ and $m = 2$. 4. The slope $m$ determines the steepness of the line. A larger $m$ means the line rises more rapidly as $x$ increases. 5. To plot these graphs in Excel: - For both functions, choose a range of $x$ values, e.g., from $-5$ to $5$. - Calculate $f(x)$ for each $x$ value using the formulas. - Create two columns: one for $x$ values and two for $f(x)$ values from each function. - Insert a scatter plot with smooth lines. - Plot both functions on the same graph to compare. 6. Interpretation: - The line for $f(x) = x + 1$ is less steep. - The line for $f(x) = 2x + 1$ is steeper because slope $m=2$ is greater. - Both cross the y-axis at $y=1$ (the intercept). This shows how changing $m$ affects the graph of a linear equation.