Equation of required line is:
[tex]y = \frac{3}{4}x-9[/tex]
Step-by-step explanation:
First of all we will convert both equations in slope-intercept form
[tex]y + 5x + 9 = 0[/tex]
Subtracting 5x from both sides
[tex]y+9 = 0-5x\\y+9 = -5x[/tex]
Subtracting 9 from both sides
[tex]y+9-9 = -5x-9\\y = -5x-9[/tex]
The y-intercept is -9.
Other equation is:
[tex]- 3x + 4y = 3[/tex]
Adding 3x on both sides
[tex]-3x+3x+4y = 3x+3\\4y=3x+3[/tex]
Dividing both sides by 4
[tex]\frac{4y}{4} = \frac{3x+3}{4}\\y = \frac{3}{4}x+\frac{3}{4}[/tex]
As the required line has y-ntercept of line y + 5x + 9 = 0
So,
b = -9
And
The line is parallel to second line, so the slopes of both will be equal
[tex]m=\frac{3}{4}[/tex]
Slope-intercept form of line is:
[tex]y=mx+b[/tex]
Putting values of b and m
[tex]y = \frac{3}{4}x-9[/tex]
Keywords: Equation of line, Slope-intercept form
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