Answer: [tex]y=2x+9[/tex]
Step-by-step explanation:
Slope of line passing through (a,b) and (c,d) = [tex]m=\dfrac{d-b}{c-a}[/tex]
⇒ Slope of line passing through (-3, -4) and (1, 4) =[tex]m=\dfrac{4-(-4)}{1-(-3)}[/tex]
[tex]\dfrac{4+4}{1+3}=\dfrac{8}{4}=2[/tex]
i.e. Slope of line passing through (-3, -4) and (1, 4) = 2
We know that the slopes of two parallel lines are equal.
Therefore , the slope of line parallel to the line passing through the points (-3, -4) and (1, 4)= 2
Also, equation of line passing through point (a,b) and has slope m :
[tex](y-b)=m(x-a)[/tex]
Then, the equation of line passing through point (-1, 7) and has slope 2 :
[tex](y-7)=2(x-(-1))\\\\y-7=2(x+1)\\\\ y-7=2x+2\\\\ y=2x+2+7=2x+9\\\\ y=2x+9[/tex]
Hence, the required equation of the line that passes through the point (-1, 7) and is parallel to the line passing through the points (-3, -4) and (1, 4).
[tex]y=2x+9[/tex]
