Question

Select the correct answer from each drop-down menu.A line passes through point (3, 7) and has a slope of 3/4.The equation of the line is _________.If point A(x, 5) lies on the line, the value of x is____. ( options for x are 33 & 1/3)

Answer 1

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:

`\begin{gathered} y-y_0=m(x-x_0) \\ y-7=(3)/(4)(x-3) \\ y-7=(3)/(4)x-(3)/(4)(3) \\ y=(3)/(4)x-(9)/(4)+7((4)/(4)) \\ y=(3)/(4)x-(9)/(4)+(28)/(4) \\ y=(3)/(4)x+(19)/(4) \end{gathered}`

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:

`\begin{gathered} y=5 \\ (3)/(4)x+(19)/(4)=5 \\ (3)/(4)x=5-(19)/(4) \\ (3)/(4)x*4=5*4-(19)/(4)*4 \\ 3x=20-19 \\ 3x=1 \\ x=(1)/(3) \end{gathered}`

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.