### About Equation of a Line Using Determinants:

We can find the equation of a line using determinants. This formula comes from our previous formula that was used to check if three points were collinear. We will change our formula slightly and remove one of the known points. This will be replaced with just x and y. We can then go through the process of finding the determinant and set this result equal to zero. From there, we can solve the equation for y and place the equation in slope-intercept form.

Test Objectives
• Demonstrate the ability to find the determinant of a matrix
• Demonstrate the ability to find the equation of a line
• Demonstrate the ability to write an equation in slope-intercept form
Equation of a Line Using Determinants Practice Test:

#1:

Instructions: write in slope-intercept form.

$$a)\hspace{.2em}(-4,1), (-3,-2)$$

$$b)\hspace{.2em}(1,-3), (0,-4)$$

#2:

Instructions: write in slope-intercept form.

$$a)\hspace{.2em}(5,3), (-1,-1)$$

$$b)\hspace{.2em}(4,3), (3,-4)$$

#3:

Instructions: write in slope-intercept form.

$$a)\hspace{.2em}(-3,2), (2,-3)$$

$$b)\hspace{.2em}(-3,-5), (-2,-3)$$

#4:

Instructions: write in slope-intercept form.

$$a)\hspace{.2em}(4,-1), (-4,-3)$$

$$b)\hspace{.2em}(0,-2), (2,4)$$

#5:

Instructions: write in slope-intercept form.

$$a)\hspace{.2em}(-1,-4), (0,1)$$

$$b)\hspace{.2em}(-1,0), (0,4)$$

Written Solutions:

#1:

Solutions:

$$a)\hspace{.2em}y=-3x - 11$$

$$b)\hspace{.2em}y=x - 4$$

#2:

Solutions:

$$a)\hspace{.2em}y=\frac{2}{3}x - \frac{1}{3}$$

$$b)\hspace{.2em}y=7x - 25$$

#3:

Solutions:

$$a)\hspace{.2em}y=-x - 1$$

$$b)\hspace{.2em}y=2x + 1$$

#4:

Solutions:

$$a)\hspace{.2em}y=\frac{1}{4}x - 2$$

$$b)\hspace{.2em}y=3x - 2$$

#5:

Solutions:

$$a)\hspace{.2em}y=5x + 1$$

$$b)\hspace{.2em}y=4x + 4$$