Question

what is the intersection point of the lines y=6x+7 and y=-9x-2? are these linear or quadratic equations

Answer 1

In general, the slope-intercept form of a linear equation is

$y=mx+b$

where m and b are constants.

Therefore, both y=6x+7 and y=-9x-2 are linear equations.

To find the intersection point, solve the system that consists of the two above linear equations

$\begin{cases}y=6x+7 \\ y=-9x-2\end{cases}$

Then,

$\begin{gathered} y=y \\ \Rightarrow6x+7=-9x-2 \\ \Rightarrow15x=-9 \\ \Rightarrow x=-\frac{9}{15}=-\frac{3}{5} \\ \Rightarrow x=-\frac{3}{5} \end{gathered}$

Substitute the value of x into the first equation, as shown below,

$\begin{gathered} x=-\frac{3}{5} \\ \Rightarrow y=6(-\frac{3}{5})+7=-\frac{18}{5}+\frac{35}{5}=\frac{17}{5} \\ \Rightarrow y=\frac{17}{5} \end{gathered}$

Thus, the intersection point is (-3/5,17/5)=(-0.6,3.4)