Answer:
The slope of the parallel line to the line 2x + 5y = -10 is [tex]-\frac{2}{5}[/tex]
Step-by-step explanation:
Parallel lines have equal slopes and different y-intercepts
To find the slope of the line from the equation of the line, then put the equation in the form y = m x + b, where
Let us solve the question
∵ The equation of a line is 2x + 5y = -10
→ Put the equation in the form above
→ Subtract x from both sides to move 2x from the left side to the
right side
∴ 2x - 2x + 5y = -10 - 2x
∴ 5y = -10x - 2x
→ Make the coefficient of y equal 1 by dividing all terms by 5
∵ [tex]\frac{5y}{5}=-\frac{10}{5}-\frac{2x}{5}[/tex]
∴ y = -2 - [tex]\frac{2}{5}x[/tex]
→ Compare it by the form of the equation above
∴ m = [tex]-\frac{2}{5}[/tex]
∴ The slope of the given line is [tex]-\frac{2}{5}[/tex]
→ We need the slope of the line which is parallel to the given line
∵ Parallel lines have the same slopes
∴ The slope of the parallel line to the line 2x + 5y = -10 is [tex]-\frac{2}{5}[/tex]
