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Sagot :
The equation of a line with slope m and y-intercept b in slope-intercept form is:
[tex]y=mx+b[/tex]On the other hand, two lines are parallel if they have the same slope.
First, find the slope of the given line by isolating y from the equation.
Next, write down the equation of a line with y-intercept -3 and with the same slope as the given line to find the equation of a line that satisfies the described characteristics.
The equation of the given line is 3x=4+5y. Isolate y:
[tex]\begin{gathered} 3x=4+5y \\ \Rightarrow3x-4=5y \\ \Rightarrow\frac{3x-4}{5}=y \\ \Rightarrow\frac{3}{5}x-\frac{4}{5}=y \\ \therefore y=\frac{3}{5}x-\frac{4}{5} \end{gathered}[/tex]Since the coefficient of x is 3/5, then, the value of the slope of the given line is 3/5.
Replace m=3/5 and b=-3 into the general equation of a line in slope-intercept form to find the equation of a line that has y-intercept of -3 and is parall
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