Answer:
Explanation:
Here, we want to graph the line with the slope of -3 passing through the point (-3,3)
To graph the line, we need two points
We need the x-intercept (point on the x-axis where y = 0) and the y-intercept (point on the y-axis where x is 0)
The equation of a straight line can be represented as:
[tex]y\text{ = mx + b}[/tex]
where m is the slope and b is the y-intercept
Using the equation above, we can write:
[tex]y\text{ = -3x + b}[/tex]
We can get b by substituting the coordinates (-3,3: where -3 will be x and 3 will be y)
[tex]\begin{gathered} 3\text{ = -3(-3) + b} \\ 3\text{ = 9 + b} \\ b\text{ = 3-9 = -6} \end{gathered}[/tex]
Now we have identified that the y-intercept is at he point (0,-6)
We have the full equation as:
[tex]y\text{ = -3x-6}[/tex]
We need to get the x-intercept now.
We can get this by substituting the value 0 for y
Mathematically, we proceed as follows:
[tex]\begin{gathered} 0\text{ = -3x - 6} \\ -3x\text{ = 6} \\ x\text{ = }\frac{-6}{3}\text{ = -2} \end{gathered}[/tex]
Thus, we have the x-intercept as (-2,0)
So to graph the line, we locate the points (0,-6) and (-2,0)
Then, we draw a line through these two points
This line will pass through the point (-3,3)
