Answer:
2x + 3y = -10
Step-by-step explanation:
First convert the line into slope intercept form to find the slope of the line.
2x + 3y = 4
3y = 4 - 2x
y = -2/3x + 4/3
The slope of the line is -2/3. Parallel lines have the same slope so the slope for a line through the point (1,-4) will be -2/3. Substitute m = -2/3 and (1,-4) into the point slope of a line.
[tex]y --4 = -\frac{2}{3}(x-1)\\y + 4 = -\frac{2}{3}(x -1)[/tex]
Now convert the line into standard form by using the distributive property.
[tex]y + 4 = -\frac{2}{3}(x -1)\\y + 4 = -\frac{2}{3}x + \frac{2}{3}\\3y + 12 = -2x + 2\\2x + 3y + 12 = 2\\2x + 3y = -10[/tex]
