Answer
y-intercept = 2
Step-by-step explanation:
[tex]\begin{gathered} The\text{ slope-intercept equation is given as} \\ y\text{ = }\frac{1}{2}x\text{ + 2} \\ \text{ Step 1: we n}eed\text{ to find the x-intercept and y-intercept} \\ To\text{ find x let y = 0} \\ 0\text{ = }\frac{1}{2}x\text{ + 2} \\ 0\text{ = }\frac{x}{2}\text{ + 2} \\ \text{ Let the common denominator} \\ 0\text{ = }\frac{x\text{ + 4}}{2} \\ \text{Cross multiply} \\ 2\cdot\text{ 0 = x + 4} \\ x\text{ + 4 =0} \\ x\text{ = 0 - 4} \\ x\text{ = -4} \\ Hence,\text{ we have (-4, 0)} \\ To\text{ find y, let x = 0} \\ y\text{ = }\frac{1}{2}x\text{ + 2} \\ y\text{ = }\frac{1}{2}(0)\text{ + 2} \\ y\text{ = 0 + 2} \\ y\text{ = 2} \\ \text{Hence, we have (0, 2)} \end{gathered}[/tex]From the given slope-intercept equation, we were able to get the points
(-4, 0 ) and (0, 2)
The next step is to plot the points on the graph.
Hence, the y-intercept is 2
