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SOLUTION
Given the question in the image, the following are the solution steps to answer the question.
STEP 1: State the slope-intercept form of the equation of a line
[tex]\begin{gathered} y=mx+c \\ where\text{ m is the slope} \\ c\text{ is the y-intercept} \end{gathered}[/tex]STEP 2: Write the given properties
[tex]\begin{gathered} slope(m)=\frac{1}{2} \\ point=(x_1,y_1)=(-1,1) \end{gathered}[/tex]STEP 3: state the formula for using a slope and a point to get the equation of a line
[tex](y-y_1)=m(x-x_1)[/tex]STEP 4: Substitute the given values
[tex]\begin{gathered} (y-1)=\frac{1}{2}(x-(-1)) \\ (y-1)=\frac{1}{2}(x+1) \\ y-1=\frac{x+1}{2} \\ Multiply\text{ through by 2} \\ 2(y-1)=x+1 \\ 2y-2=x+1 \\ 2y=x+1+2 \\ 2y=x+3 \\ y=\frac{x+3}{2} \\ y=\frac{x}{2}+\frac{3}{2} \\ y=\frac{1}{2}x+\frac{3}{2} \end{gathered}[/tex]Hence, the slope-intercept form of the equation of the line with the properties is given as:
[tex]y=\frac{1}{2}x+\frac{3}{2}[/tex]
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