Explanation:
The line
![y = -3x + 3](https://img.qammunity.org/2022/formulas/mathematics/college/bp5zs2y09yrkcy5fbxdeppxkrikvxrzu93.png)
Is in point Slope form. This means the Slope and the y intercept are visible in the equation 9f the form
![y = mx + b](https://img.qammunity.org/2022/formulas/mathematics/high-school/hi7nib56czgdtaz3ud2tuzvr49eqo8cnyj.png)
Where m is the Slope of the line and b is the y coordinate of the y intercept.
To determine the y intercept, assume x = 0, then - 3x = 0, so y = 3 and x = 0 (0,3}
From that point you can find the next point by choosing a value for x in the given equation to find a corresponding y.
Substitute 1 for x and get 0 for y, (1,0)
Substitue 2 for x and get - 3 for y, (2,-3)
To answer the questions use the supplied coordinates in the original equation.
#1. (-1,6)
![6 = - 3( - 1) + 3](https://img.qammunity.org/2022/formulas/mathematics/college/sdxfucgu0d3niux4iemndubvce191qt39s.png)
![6 = 3 + 3](https://img.qammunity.org/2022/formulas/mathematics/college/h0qi9e54wjt2xqzjh2ph1owktek6kiorrt.png)
This is a true statement, so the line does pass through this point.
#2 (12,-33)
![- 33 = - 3(12) + 3](https://img.qammunity.org/2022/formulas/mathematics/college/gfsi45j44fddoqp95kx6xef3yl0fa7of81.png)
![- 33 = - 36 + 3](https://img.qammunity.org/2022/formulas/mathematics/college/2slihjqq0n4g8o2xwcyb49jkjkgnn35o06.png)
Again, the statement is true, so the line passes through the point.
#3 (2,9)
![9 = - 3(2) + 3](https://img.qammunity.org/2022/formulas/mathematics/college/pi74gla1wwdapyzl4v1yzeqmmhk967vv5i.png)
![9 = - 6 + 3](https://img.qammunity.org/2022/formulas/mathematics/college/56fnxqw28ocgll6vgdehxzhpx28unk85w6.png)
This is a false {untrue} statement, so the point does not sit on the line.