ANSWER
The line that is parallel to [tex]y=4x-6[/tex] through [tex](12,10)[/tex] is [tex]y=2x-14[/tex].
EXPLANATION
The equation that is parallel to the line [tex]y=4x-6[/tex] has a slope that is equal to the slope of this line.
By comparing this equation to the general slope intercept form,
[tex]y=mx+c[/tex],this line has slope [tex]m=2[/tex].
Hence the line parallel to this line also has slope [tex]m=2[/tex].
Let [tex]y=mx+b[/tex] be the equation of the line parallel to the line
[tex]y=4x-6[/tex]
We can substitute [tex]m=2[/tex] to obtain;
[tex]y=2x+b[/tex]
If the line passes through the point [tex](12,10)[/tex],then this point must satisfy its equation.
We substitute [tex]x=12[/tex] and [tex]y=10[/tex] to obtain;
[tex]10=2(12)+b[/tex]
We this equation for [tex]b[/tex].
[tex]\Rightarrow 10=24+b[/tex]
[tex]\Rightarrow 10-24=b[/tex]
[tex]\Rightarrow -14=b[/tex]
We substitute this value of [tex]b=-14[/tex] in to [tex]y=2x+b[/tex] to get;
[tex]y=2x+-14[/tex].
Hence the equation of the line that is parallel to [tex]y=4x-6[/tex] through [tex](12,10)[/tex] is [tex]y=2x-14[/tex].
