We have a line that passes through (3, 7) and has a slope of 3/4.
We can find the equation by writing it in slope-point form and then rearrange it:
[tex]\begin{gathered} y-y_0=m(x-x_0) \\ y-7=\frac{3}{4}(x-3) \\ y-7=\frac{3}{4}x-\frac{3}{4}(3) \\ y=\frac{3}{4}x-\frac{9}{4}+7(\frac{4}{4}) \\ y=\frac{3}{4}x-\frac{9}{4}+\frac{28}{4} \\ y=\frac{3}{4}x+\frac{19}{4} \end{gathered}[/tex]
The equation of the line is y = 3/4*x + 19/4.
If point A = (x,5) belongs to the line, we can find x as:
[tex]\begin{gathered} y=5 \\ \frac{3}{4}x+\frac{19}{4}=5 \\ \frac{3}{4}x=5-\frac{19}{4} \\ \frac{3}{4}x*4=5*4-\frac{19}{4}*4 \\ 3x=20-19 \\ 3x=1 \\ x=\frac{1}{3} \end{gathered}[/tex]
Answer:
The equation of the lineis y = 3/4*x + 19/4.
If point A(x,5) lies on the line, the value of x is 1/3.
