Answer:
B
Step-by-step explanation:
To find the equation, we can use the point-slope form:
[tex]y-y_1=m(x-x_1)[/tex]
Where m is the slope and (x₁, y₁) is a point.
First, we will need to find the slope. Since we have two points, we can use the slope formula:
[tex]\displaystyle m=\frac{y_2-y_1}{x_2-x_1}[/tex]
Let (2, -1) be (x₁, y₁) and let (0, 5) be (x₂, y₂). Substitute and evaluate:
[tex]\displaystyle m=\frac{5-(-1)}{0-2}=6/-2=-3[/tex]
Therefore, the slope m is -3.
Now, we can use the point-slope form. We also need a point. Let’s use (2, -1) for consistency. So, we will substitute -3 for m and (2, -1) for (x₁, y₁). This yields:
[tex]y-(-1)=-3(x-2)[/tex]
We will now convert this to slope-intercept form. Simplify the left and distribute the right:
[tex]y+1=-3x+6[/tex]
Subtract 1 from both sides. Therefore, our equation is:
[tex]y=-3x+5[/tex]
Thus, our answer is B.
