write the equation of the line in slope intercept form.

Explanation:

Step1: Recall slope - intercept form

The slope - intercept form of a line is $y = mx + b$, where $m$ is the slope and $b$ is the y - intercept.

Step2: For the first graph (problem 4)

Pick two points, say $(0,1)$ and $(1,3)$. The slope $m=\frac{y_2 - y_1}{x_2 - x_1}=\frac{3 - 1}{1 - 0}=2$. The y - intercept $b = 1$ (where the line crosses the y - axis). So the equation is $y=2x + 1$.

Step3: For the second graph (problem 5)

The line is horizontal. For a horizontal line, the slope $m = 0$. The line crosses the y - axis at $y=-4$. So the equation is $y=-4$ (since $y=0x-4$).

Step4: For the third graph (problem 6)

Pick two points, say $(0,4)$ and $(4,2)$. The slope $m=\frac{y_2 - y_1}{x_2 - x_1}=\frac{2 - 4}{4 - 0}=-\frac{1}{2}$. The y - intercept $b = 4$. So the equation is $y=-\frac{1}{2}x + 4$.

Answer:

Problem 4: $y = 2x+1$ Problem 5: $y=-4$ Problem 6: $y=-\frac{1}{2}x + 4$