Answer:
[tex]y-3=\frac{12}{5} (x-2)[/tex] or [tex]y=\frac{12}{5}x - \frac{9}{5}[/tex]
Step-by-step explanation:
First, rearrange the equation of the given line to the form y=mx+b
This makes it easier to identify the slope
12x-5y=2
5y=12x-2
y= (12x/5)-(2/5)
In this form, it is easier to see that the slope is m= 12/5
Since the lines are parallel, the slope is the same for both equations
Now, use the point-slope equation to find the equation of the parallel line
[tex]y-y_1= m (x-x_1)[/tex]
Substitute the values of the given coordinate point (2,3) in for X1 and Y1
Y1=3
X1=2
Now, substitute the value of the slope into the equation too
The equation now becomes :
[tex]y-3=\frac{12}{5} (x-2)[/tex]
The equation can be left in that form or simplified into the y=mx+b form
To simplify:
[tex]y-3=\frac{12}{5} (x-2)[/tex]
[tex]y-3=\frac{12}{5}x - \frac{24}{5}[/tex]
[tex]y=\frac{12}{5}x - \frac{24}{5}+3[/tex]
[tex]y=\frac{12}{5}x - \frac{9}{5}[/tex]
