Join the growing community of curious minds on IDNLearn.com. Our platform provides accurate, detailed responses to help you navigate any topic with ease.

Use algebra to find the point at which the line


intersects the line


.


Use Algebra To Find The Point At Which The Line Intersects The Line class=

Sagot :

Answer:

[tex](3\ ,\ \frac{17}{4})[/tex]

Step-by-step explanation:

  • To find the intersection point you need to set the two equations equal to each other and solve for x .

here is how to do it :

[tex]$\begin{aligned} & -\frac{2}{3} x+\frac{9}{4}=\frac{7}{5} x+\frac{169}{20} \\ & \Leftrightarrow-\frac{2}{3} x-\frac{7}{5} x=\frac{169}{20}-\frac{9}{4} \\ & \Leftrightarrow \frac{-10 x-21 x}{15}=\frac{169-45}{20} \\ & \Leftrightarrow-\frac{31}{15} x=\frac{124}{20} \\ & \Leftrightarrow x=\frac{124}{20} \times\left(-\frac{15}{31}\right) \\ & \Leftrightarrow x=-\frac{1860}{620} \\ & \Leftrightarrow x=-3\end{aligned}$[/tex]

  • Now, you can plug it back into either of the original equations to find y.

let’s use g(x) :

[tex]$\begin{aligned} g(-3) & =-\frac{2}{3} \times(-3)+\frac{9}{4} \\ & =2+\frac{9}{4} \\ & =\frac{8+9}{4} \\ & =\frac{17}{4} \\ & =4.25\end{aligned}$[/tex]

Therefore, the coordinates of the intersection points are :

[tex](3\ ,\ \frac{17}{4})[/tex]