The points $P = (x_1, y_1)$ and $Q(3, 4)$ are on the line $y=kx+m$. What are the coordinates of point $P$ ? Given
$m = -2$
$P$ is on the line $x=2$
We need both information together to solve the problem. I don't know how to approach this question. Can anyone help me?
Notice, substituting given value $m=-2$ in the equation of the line is $y=kx+m$, we get $$y=kx-2$$ since the point $Q(3, 4)$ lies on the above line hence it will satisfy the above equation as follows $$4=k(3)-2\implies k=2$$ hence substituting $k=2$, the equation of line is $y=2x-2$
Now, the point $P(x_1, y_1)$ lies on the line $x=2$ hence its x-coordinate is $x_1=2$. Since $P(2, y_1)$ also lies on the line: $y=2x-2$ hence substituting $x=x_1=2$ & $y=y_1$, we get $$y_1=2(2)-2=2$$ hence, the coordinates of the point $P$ are $\color{blue}{x_1=2,\ \ y_1=2}$ i.e. $\color{red}{P(2, 2)}$