To solve the exercise you can use the point-slope formula, that is,
[tex]\begin{gathered} $y-y_1=m(x-x_1)$ \\ \text{ Where m is the slope of the line and } \\ (x_1,y_1)\text{ is a point through which the line passes} \end{gathered}[/tex]
So, in this case, you have
[tex]\begin{gathered} m=\frac{3}{4} \\ (x_1,y_1)=(3,7) \end{gathered}[/tex][tex]\begin{gathered} y-y_1=m(x-x_1) \\ \text{ Replace} \\ y-7=\frac{3}{4}(x-3) \\ y-7=\frac{3}{4}x-3\cdot\frac{3}{4} \\ y-7=\frac{3}{4}x-\frac{9}{4} \\ \text{ Add 7 from both sides of the equation} \\ y-7+7=\frac{3}{4}x-\frac{9}{4}+7 \\ y=\frac{3}{4}x+\frac{19}{4} \end{gathered}[/tex]
Therefore, the equation of the line is
[tex]y=\frac{3}{4}x+\frac{19}{4}[/tex]
Finally, to find the x-coordinate of point A, replace y = 5 into the equation of the line you just found and solve for x
[tex]\begin{gathered} y=\frac{3}{4}x+\frac{19}{4} \\ 5=\frac{3}{4}x+\frac{19}{4} \\ \text{ Subtract 19/4 from both sides of the equation} \\ 5-\frac{19}{4}=\frac{3}{4}x+\frac{19}{4}-\frac{19}{4} \\ \frac{1}{4}=\frac{3}{4}x \\ \text{ Multiply by 4/3 on both sides of the equation} \\ \frac{1}{4}\cdot\frac{4}{3}=\frac{4}{3}\cdot\frac{3}{4}x \\ \frac{1}{3}=x \end{gathered}[/tex]
Therefore, if point A(x,5) lies on the line, the value of x is 1/3.
