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Answer:
8x - 5y = - 30
Step-by-step explanation:
The equation of a line in slope- intercept form is
y = mx + c ( m is the slope and c the y- intercept )
Rearrange 8x - 5y = 2 into this form
Subtract 8x from both sides
- 5y = - 8x + 2 ( divide all terms by - 5 )
y = x -
← in slope- intercept form
with slope m =
• Parallel lines have equal slopes, hence
y = x + c ← is the partial equation of the parallel line
To find c substitute (- 5, - 2) into the partial equation
- 2 = - 8 + c ⇒ c = - 2 + 8 = 6
y = x + 6 ← in slope- intercept form
Multiply through by 5
5y = 8x + 30 ( subtract 5y from both sides )
0 = 8x - 5y + 30 ( subtract 30 from both sides )
8x - 5y = - 30 ← in standard form