Question

Here is a linear equation: y=1/4x+5/41. Are (1, 1.5) and (12,4) solutions to the equation?A. Both (1, 1.5) and (12,4) are solutions to the equation.B. Neither (1, 1.5) and (12,4) are solutions to the equation.C. (1, 1.5) is a solution but (12,4) is not.D. (12,4) is a solution to the equation but (1, 1.5) is not.Explain your reasoning.3. Find the x-intercept of the graph of the equationExplain or show your reasoning.

Answer 1

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:

$\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}$$\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}$

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:

$\begin{gathered} y=\frac{1}{4}x+\frac{5}{4} \\ \rightarrow0=\frac{1}{4}x+\frac{5}{4}\rightarrow0=\frac{x+5}{4}\rightarrow0=x+5\rightarrow-5=x \\ \rightarrow x=-5 \end{gathered}$

Therefore, the x-intercept is -5