Answer:
[tex]\sf\longrightarrow \boxed{\pink{\sf 3x + 4y -8=0}}[/tex]
Step-by-step explanation:
We need to write the slope intercept form of the equation which passes through (4,-1) and parallel to the line y = -3/4x .
We know that the line parallel to a given line has the same slope . Therefore the slope of the line will be , ( on comparing to Slope Intercept Form ) .
[tex]\sf\longrightarrow Slope =\dfrac{-3}{4}[/tex]
On using point slope form ,
[tex]\sf\longrightarrow y-y_1= m ( x - x_1) [/tex]
Substitute the respective values ,
[tex]\sf\longrightarrow y - (-1) = \dfrac{-3}{4}( x - 4 ) [/tex]
Simplify ,
[tex]\sf\longrightarrow y +1 = \dfrac{-3}{4}x + 3 [/tex]
Multiply both sides by 4 ,
[tex]\sf\longrightarrow 4y + 4 = -3x + 12 [/tex]
Put all terms on same side , i.e. on LHS ,
[tex]\sf\longrightarrow \boxed{\pink{\sf 3x + 4y -8=0}}[/tex]
Hence the equation of the line is 3x + 4y - 8 = 0.
