Answer:
[tex]\displaystyle y-1=-\frac{3}{2}x[/tex]
Step-by-step explanation:
Givens
We are given that the equation we wish to determine has a slope of:
[tex]\displaystyle -\frac{3}{2}[/tex]
This is also referred to as m.
We are also told that the equation will pass through the point:
[tex](0, 1)[/tex]
This can be written as:
The final equation must be written in the point-slope form:
[tex]y-y_1=m(x-x_1)[/tex]
Solve
First, substitute the slope as m into the formula:
[tex]\displaystyle y-y_1=-\frac{3}{2}(x-x_1)[/tex]
Then, substitute x₁ and y₁ into the formula:
[tex]\displaystyle y-1=-\frac{3}{2}(x-0)[/tex]
Finally, simplify by removing the redundant constant:
[tex]\displaystyle y-1=-\frac{3}{2}x[/tex]
Therefore, the final equation in point-slope form is:
[tex]\displaystyle \boxed{y-1=-\frac{3}{2}x}[/tex]
