Question

ТА12Select the correct answer from each drop-down menu.3A line passes through point (3, 7) and has a slope of 4.The equation of the line is.......If point A(x, 5) lles on the line, the value of x is......

Answer 1

To solve the exercise you can use the point-slope formula, that is,

`\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}`

So, in this case, you have

`\begin{gathered} m=(3)/(4) \\ (x_1,y_1)=(3,7) \end{gathered}`
`\begin{gathered} y-y_1=m(x-x_1) \\ \text{ Replace} \\ y-7=(3)/(4)(x-3) \\ y-7=(3)/(4)x-3\cdot(3)/(4) \\ y-7=(3)/(4)x-(9)/(4) \\ \text{ Add 7 from both sides of the equation} \\ y-7+7=(3)/(4)x-(9)/(4)+7 \\ y=(3)/(4)x+(19)/(4) \end{gathered}`

Therefore, the equation of the line is

`y=(3)/(4)x+(19)/(4)`

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

`\begin{gathered} y=(3)/(4)x+(19)/(4) \\ 5=(3)/(4)x+(19)/(4) \\ \text{ Subtract 19/4 from both sides of the equation} \\ 5-(19)/(4)=(3)/(4)x+(19)/(4)-(19)/(4) \\ (1)/(4)=(3)/(4)x \\ \text{ Multiply by 4/3 on both sides of the equation} \\ (1)/(4)\cdot(4)/(3)=(4)/(3)\cdot(3)/(4)x \\ (1)/(3)=x \end{gathered}`

Therefore, if point A(x,5) lies on the line, the value of x is 1/3.