1. **Problem 1:** Graph the linear function $y = 4x + 3$. - The slope of the line is the coefficient of $x$, which is $4$. - The $y$-intercept is the constant term, which is $3$. This means the line crosses the $y$-axis at $(0,3)$. 2. Identify three points on the line by choosing values for $x$ and calculating $y$: - For $x=0$: $y = 4(0) + 3 = 3$ giving point $(0,3)$. - For $x=1$: $y = 4(1) + 3 = 7$ giving point $(1,7)$. - For $x=-1$: $y = 4(-1) + 3 = -4 + 3 = -1$ giving point $(-1,-1)$. 3. Plot points $(0,3)$, $(1,7)$, and $(-1,-1)$ on graph paper and draw a straight line through them. Label the points and the line. 4. **Problem 2:** Graph the quadratic function $y = x^2 + 2x + 1$. - This is a quadratic function that can be factored as $y = (x+1)^2$. - The vertex is at $x = -1$, $y = 0$ since $(x+1)^2 = 0$ at $x=-1$. 5. Create a table of values with at least three points: | $x$ | $y = (x+1)^2$ | |---|---| | -2 | $(-2+1)^2 = (-1)^2 = 1$ | | -1 | $(-1+1)^2 = 0^2 = 0$ | | 0 | $(0+1)^2 = 1^2 = 1$ | 6. Plot points $(-2,1)$, $(-1,0)$, and $(0,1)$ on the graph paper. Draw the parabola passing through these points opening upwards. Label the points and vertex. This completes the graphing of both functions with proper points and labels.