Chapter B, Problem 1E

To determine

To find: The equation of the line that passes through the point $\left(6,4\right)$ and has a slope $m=-\frac{2}{3}$.

Answer to Problem 1E

Solution: The equation of the line which passes through the point $\left(6,4\right)$ and slope $m=-\frac{2}{3}$ is $y=-\frac{2}{3}x+8$.

Explanation of Solution

Given: The points through which the line passes is $\left(6,4\right)$ and the slope is $m=-\frac{2}{3}$.

Formula used:

The formula of straight line passing through the given point and having the given slope is,

$\left(y-y_1\right)=m\left(x-x_1\right)$

Where,

• $y_1$ is the point on y-axis.

• $x_1$ is the point on x-axis.

Calculations:

Substitute 4 for $y_1$, 6 for $x_1$ and $-\frac{2}{3}$ for m to find the equation of the line.

$\begin{array}{c}\left(y-4\right)=-\frac{2}{3}\left(x-6\right)\\ \left(y-4\right)=-\frac{2}{3}x+4\\ y=-\frac{2}{3}x+8\end{array}$

The equation of line that passes through the given point and has the given slope is $y=-\frac{2}{3}x+8$.