Chapter 7.5, Problem 68E

Equation of a line. Three points $\left(x,y\right)$, $\left(x_1,y_1\right)$ and $\left(x_2,y_2\right)$

all lie on the same line if and only if $D=\left|\begin{array}{ccc}x& y& 1\\ x_1& y_1& 1\\ x_2& y_2& 1\end{array}\right|=0$

.Therefore, the equation $\left|\begin{array}{ccc}x& y& 1\\ x_1& y_1& 1\\ x_2& y_2& 1\end{array}\right|=0$. In other words, a point $P\left(x,y\right)$

lies on the line passing through the points $\left(x_{1,}{y}_1\right)$ and $\left(x_2,y_2\right)$. If and only if the determinant $D=0$, is an equation of the line passing through the points $\left(x_{1,}{y}_1\right)$ and $\left(x_2,y_2\right)$. Use determinants to write an equation of the line passing through the given points. Then evaluate the determinant and write the equation of the line in slope-intercept form.

$\left(0,4\right)$, $\left(1,1\right)$