Question

8. Write the equation of the line that is parallel to the line 2x + 5y = 15 and passes through the

Answer 1

Answer:

$\sf y = \bold -\frac{2}{5} x -3$

Explanation:

part A identification for slope:

$\sf 2x + 5y = 15$

$\sf 5y = -2x + 15$

$\sf y = \frac{-2x + 15}{5}$

$\sf y = -\frac{2 }{5} x+3$

comparing with slope intercept form: y = mx + b

we can find that here the slope is $\bold -\frac{2}{5}$

part B, solving the equation:

if the line is parallel, then the slope will be same.

given coordinates: ( - 10, 1 )

using the equation:

y - y₁ = m( x - x₁ )

$\sf y - 1 = \bold -\frac{2}{5} (x --10)$

$\sf y = \bold -\frac{2}{5} x -4 + 1$

$\sf y = \bold -\frac{2}{5} x -3$

Extra information:

check the image below. this proves that the line is parallel and passes through point (-10, 1). the blue line is question line and red the answer line.

Answer 2

Solution:

Step-1: Convert the line into slope intercept form.

• 2x + 5y = 15
• => 5y = -2x + 15
• => y = -0.4x + 3

Step-2: Use the point slope form formula.

• y - y₁ = m(x - x₁)
• => y - 1 = -0.4{x - (-10)}
• => y - 1 = -0.4{x + 10}
• => y - 1 = -0.4x - 4
• => y = -0.4x - 3