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Sagot :
To find if any given point is a solution for the linear equation, simply plug in the x and y values given and check if the equality stands, as following:
[tex]\begin{gathered} y=\frac{1}{4}x+\frac{5}{4} \\ (1,1.5) \\ \rightarrow1.5=\frac{1}{4}(1)+\frac{5}{4}\rightarrow1.5=\frac{6}{4}\rightarrow1.5=1.5✅ \end{gathered}[/tex][tex]\begin{gathered} y=\frac{1}{4}x+\frac{5}{4} \\ (12,4) \\ \rightarrow4=\frac{1}{4}(12)+\frac{5}{4}\rightarrow4=3+\frac{5}{4}\rightarrow4=4.25✘ \end{gathered}[/tex]Thereby the answer is:
C. (1, 1.5) is a solution but (12, 4) is not
Now, to find the x-intercept just make y = 0 and clear x, as following:
[tex]\begin{gathered} y=\frac{1}{4}x+\frac{5}{4} \\ \rightarrow0=\frac{1}{4}x+\frac{5}{4}\rightarrow0=\frac{x+5}{4}\rightarrow0=x+5\rightarrow-5=x \\ \rightarrow x=-5 \end{gathered}[/tex]Therefore, the x-intercept is -5
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