What is an equation of the line that passes through the point (-2,-4)and is parallel to the line 5x+2y=6

Answer 1

The attached video explains all steps involved.

1. Solve the equation for "y" to reveal slope "m".
2. 5x + 2y = 6
3. -5x -5x {Subtract 5x from both sides}
4. 2y =-5x+6
5. 2 2 2 {Divide each term by 2}
6. y = -5/2 x +3
7. y = m x + b {Slope-intercept form of equation}
8. m = -5/2 {Slope from equation above}
9. Slopes from parallel lines are equal
10. m = -5/2 {New slope = Above slope}
11. Use point (-2 , -4) and new slope to find new equation
12. y - y₁ = m (x - x₁) {Point-Slope Form of Equation}
13. y-(-4 )= -5/2 (x - (-2)) {Plug in new slope and point x₁= -2, y₁= -4. Then solve for y }
14. y + 4 = -5/2 (x + 2) {Simplify the double negatives}
15. y + 4 = -5/2 x - 5 {Distribute -5/2 inside parenthesis. See video.}
16. - 4 - 4 {Subtract 4 from both sides to solve for y}
17. y = -5/2 x - 9 {YOUR ANSWER!!! }

Answer 2

Parallel lines have the same slope.

step 1: solve nfopr y to get the slope.

5x + 2y =6

2y = 6 - 5x

y=6/2 - (5x)/2.

y = 3-(2.5)x

y = -(2.5)x + 3

So you know, the slope (-2.5) and 1 x(-2) and y(-4) that work for your new line.

The best equation is the "point-slope" form:

(y-y₁) = m(x-x₁)

(y-[-4])=[-2.5](x-[-2])

y+4= -2.5x + 5

y = -2.5x +5 - 4

y = -2.5x + 1