Answer:
[tex]2x+3y=-10[/tex]
Step-by-step explanation:
We can write the equation of a line in 3 different forms including slope intercept, point-slope, and standard depending on the information we have. We have a point given and a slope we can find from the standard equation. We will chose point-slope since we have a point and can find the slope. We can then convert into standard.
Point slope:[tex]y-y_1=m(x-x_1)[/tex]
We must find the slope by converting the standard form into slop-intercept.
[tex]2x+3y=4\\2x-2x+3y=4-2x\\3y=4-2x\\\frac{3y}{3} =\frac{4-2x}{3}[/tex]
We rearrange in y=mx+b form to [tex]y=-\frac{2}{3}x+\frac{4}{3}[/tex].
Since parallel lines have the same slope [tex]m=-\frac{2}{3}[/tex] is the slope for our line. We will now use point slope form.
We will substitute [tex]m=-\frac{2}{3}[/tex] and [tex]x_1=1\\y_1=-4[/tex].
[tex][tex]y+4=-\frac{2}{3}x+\frac{2}{3} \\y+4-4=-\frac{2}{3}x+\frac{2}{3}-4\\y=-\frac{2}{3}x+\frac{2}{3}-4\\y=-\frac{2}{3}x+\frac{2}{3}-\frac{12}{3} \\\frac{2}{3}x+y=-\frac{2}{3}x+-\frac{2}{3}x-\frac{10}{3}[/tex][/tex]
This simplifies to [tex]\frac{2}{3}x+y=-\frac{10}{3}[/tex].
To be in standard form, the coefficients of x and y must not be 0 or any fractions. The coefficient of x muxt be positive. To meet these requirements, we multiply the entire equation by 3.
[tex]3(\frac{2}{3}x+y=-\frac{10}{3})\\\frac{6}{3}x+3y=-\frac{30}{3}\\2x+3y=-10[/tex]
