Respuesta :
Answer:
[tex]y=3x+2[/tex]
Step-by-step explanation:
Given equation:
[tex]y=3x+1[/tex]
To find the equation of line parallel to the line of the given equation and passes through point (-2,4).
Applying slope relationship between parallel lines.
[tex]m_1=m_2[/tex]
where [tex]m_1[/tex] and [tex]m_2[/tex] are slopes of parallel lines.
For the given equation in the form [tex]y=mx+b[/tex] the slope [tex]m_2[/tex]can be found by comparing [tex]y=3x+1[/tex] with standard form.
∴ [tex]m_2=3[/tex]
∴ [tex]m_1=3[/tex]
The line passes through point (-2,4)
Using point slope form:
[tex]y_-y_1=m(x_-x_1)[/tex]
Where [tex](x_1,y_1)\rightarrow (-2,4)[/tex] and [tex]m=m_1=3[/tex]
So,
[tex]y-(-4)=3(x-(-2))[/tex]
Simplifying
[tex]y+4=3(x+2)[/tex]
Using distribution.
[tex]y+4=(3x)+(2\times 3)[/tex]
[tex]y+4=3x+6[/tex]
Subtracting 4 from both sides.
[tex]y+4-4=3x+6-4[/tex]
[tex]y=3x+2[/tex]
Thus the equation of line in standard form is given by:
[tex]y=3x+2[/tex] (Answer)
