Respuesta :
Step-by-step explanation:
line A can be written as y1= 3/4.x -5/4
line B is a linear function : y2= ax +b
4a+b=7 and -a +b =3 so a=4/5 and b=19/5
so y2=4/5x +19/5
so they are not parallel
Line A goes through (0,-5/4) and (1,-1/2)
Gradient of line A = G1= (-1/2 - (-5/4))/(1-0) =3/4=0.75
Gradient of line B= G2= (7/3)/(4-(-1))=4/5=0.8
The Line A and Line B are not parallel to each other.
Equation of line :
The equation of line A is,
[tex]3x-4y=5[/tex]
Now write in slope intercept form,
[tex]3x-4y=5\\\\4y=3x-5\\\\y=\frac{3}{4} x-\frac{5}{4}[/tex]
Slope of line A is [tex]\frac{3}{4}[/tex].
Equation of line B is,
[tex]y-7=\frac{3-7}{-1-4}(x-4) \\\\y-7=\frac{4}{5} x-\frac{16}{5}\\ \\y=\frac{4}{5} x+\frac{19}{5}[/tex]
Slope of line B is [tex]\frac{4}{5}[/tex]
Since, the slope of both line A and B are different. therefore, Line A and Line B are not parallel to each other.
Learn more about the parallel lines here:
https://brainly.com/question/24607467
