This table gives a few (x, y) pairs of a line in the coordinate plane. x y22 3627 5432 72What is the x-intercept of the line?

Answer:(12,0)Step-by-step explanation:Let us find the equation of the line with the help of two point form of a lineHere take any two coordinates say (22,36) and (27,54)The two point form says[tex]\frac{y-y_{1}}{x-x_{1}}=\frac{y_{2}-y_{1}}{x_{2}-x_{1}}[/tex]Putting the values in above formula [tex]\frac{y-36}{x-22}=\frac{54-36}{27-22}[/tex][tex]\frac{y-36}{x-22}=\frac{18}{5}[/tex][tex]y-36=\frac{18}{5} \times (x-22)[/tex][tex]y=\frac{18}{5} \times (x-22) + 36[/tex]In order to determine the x intercept we put y = 0 and solve it for x [tex]0-36=\frac{18}{5} \times (x-22)[/tex][tex]-36 \times \frac{5}{18}=(x-22)[/tex][tex]-10=x-22[/tex]adding 22 on both sides we getx=12Hence the x intercept is 12