Chapter 4.2, Problem 5E

To determine

To write the equationof a line with point as $\left(7,-4\right)$ and slope as $m=-6$ .

Answer to Problem 5E

The equation of the line is $\left(y+4\right)=-6\left(x-7\right)$ .

Explanation of Solution

Given:

  Slope $=$$m=-6$

  Point $=$$\left(7,-4\right)$

Formula Used:

The equation of a line in point-slope form is written as $\left(y-y_1\right)=m\left(x-x_1\right)$ where m is the slope.

Calculation:

Given:

  Slope $=$$m=-6$

  Point $=$$\left(7,-4\right)$

As per the above definition, we have equation of the line as

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

  $\left(y-\left(-4\right)\right)=-6\left(x-7\right)$

Solving the above equation, we have:

  $\left(y+4\right)=-6\left(x-7\right)$

Thus, the equation of the line is $\left(y+4\right)=-6\left(x-7\right)$ .

Conclusion:

Hence, the equation of the line is $\left(y+4\right)=-6\left(x-7\right)$ .