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Sagot :
Answer:
The equation of the line is [tex]y = -\frac{3x}{5} + 13[/tex]
Step-by-step explanation:
Equation of a line:
The equation of a line has the following format:
[tex]y = mx + b[/tex]
In which m is the slope and b is the y-intercept.
Parallel lines:
If two lines are parallel, their slopes are the same.
Parallel to 3x + 5y = 11
Placing in the standard format:
[tex]5y = -3x + 11[/tex]
[tex]y = -\frac{3x}{5} + \frac{11}{5}[/tex]
So the slope is [tex]-\frac{3}{5}[/tex], which means that the desired equation is:
[tex]y = -\frac{3x}{5} + b[/tex]
Passes through the point (15, 4).
This mean that when [tex]x = 15, y = 4[/tex]. We use this to find b. So
[tex]y = -\frac{3x}{5} + b[/tex]
[tex]4 = -\frac{3(15)}{5} + b[/tex]
[tex]-9 + b = 4[/tex]
[tex]b = 13[/tex]
So
[tex]y = -\frac{3x}{5} + 13[/tex]
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