Respuesta :
Answer:
[tex]\text{The equation represent the line that is parallel to 3x - 4y = 7 and passes through the point (-4, -2) is 3x-4y=-4}[/tex]
Step-by-step explanation:
Given the equation 3x - 4y = 7
we have to find the equation which represent the line that is parallel to 3x - 4y = 7 and passes through the point (-4, -2)
As parallel lines have same slope therefore we find the slope of given line
[tex]3x-4y=7[/tex]
[tex]4y=3x-7[/tex]
[tex]y=\frac{3}{4}x-\frac{7}{4}[/tex]
Comparing above equation with general equation y=mx+c, where m is slope
⇒ [tex]m=\frac{3}{4}[/tex]
[tex]\text{The equation of line having slope }\frac{3}{4}\text{ and passing through the point (-4,-2) is}[/tex]
[tex]y-y'=m(x-x')[/tex]
[tex]y-(-2)=\frac{3}{4}(x-(-4))[/tex]
[tex]y+2=\frac{3}{4}(x+4)[/tex]
[tex]4y+8=3x+12[/tex]
[tex]3x-4y=-4[/tex]
which is required equation.
Option 2 is correct.
