The first step that we must take before attempting to solve the problem is to understand what the problem statement is asking us to do and what is given to us to help accomplish that goal. Looking at the problem statement we can see that we are being asked to write an equation. The information that is provided to us is the slope of the line and a point through which the line crosses.
Now that we have determine the important aspects of the problem, we can move onto the actual calculations of the problem which can start off by us plugging information into the point-slope form. But before plugging in the values we should understand what makes up the form.
- [tex]y_1[/tex] ⇒ This variable captures the y-coordinate of the coordinate that is provided in the problem through which the line crosses.
- [tex]m[/tex] ⇒ This variable capture the slope of the line that we will need to determine.
- [tex]x_1[/tex] ⇒ This variable captures the x-coordinate of the coordinate that is provided in the problem through which the line crosses.
Plug in values
- [tex]y-y_1 = m(x - x_1)[/tex]
- [tex]y-1.5= -2.5(x - 2)[/tex]
Now that we have plugged in all of the values into the variables that need to be altered we can begin distributing on the right side and then solving for y.
Distribute
- [tex]y-1.5= -2.5(x - 2)[/tex]
- [tex]y-1.5= (-2.5*x) + (-2.5* - 2)[/tex]
- [tex]y-1.5= -2.5x + 5[/tex]
We are almost done with solving for y and the only step that we have left is to add 1.5 to both sides. This will remove it from the left side and isolate y which will give us the equation of the line that we need.
Add 1.5 to both sides
- [tex]y+(-1.5 + 1.5)= -2.5x + (5+ 1.5)[/tex]
- [tex]y= -2.5x + (5+ 1.5)[/tex]
- [tex]y= -2.5x + 6.5[/tex]
Now that we have fully simplified the expression using the slope and point that was given to us, we were able to determine that the equation that represents that line is y = -2.5x + 6.5
