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

First you need to find the slope from the given equation. To do this we must solve the equation for y.

5x-2y=6

Add 2y to both sides:

5x=6+2y

Subtract 6 from both sides:

5x-6=2y

Now divide everything by 2 to get y by itself.

(5/2)x-3=y

Your slope for a parallel line is the number in front of x. In this case it will be 5/2.

Now when can use the point slope equation.

y-(-4)=(5/2)(x-(-2))

y+4=(5/2)(x+2)

Multiply both sides by 2 to get rid of the fraction.

2y+8=5x+10

now solve for y

2y = 5x +2

y=(5/2)x+1

Answer 2

Hello, Iman.

Since the line you are looking for is parallel to 5x - 2y = 6, then you need to find the slope (m) of that line.

We can put that equation in slope-intercept form, y = mx + b, by solving for y:

5x - 2y = 6

5x -2y + 2y = 6 + 2y

5x - 6 = 6 - 6 + 2y

5x - 6 = 2y

or

2y = 5x - 6

Now, solve for y by dividing both sides by 2:

y = (5/2)x - 3

Now, the equation is in slope-intercept form and we can see that the slope (m) is 5/2

Since the new line is parallel to this line, it, too will have a slope of 5/2

Now we can use the point-slope form to find the new line.

(y - y₁) = m(x - x₁)

Now substitute the slope (m ) which is 5/2:)

(y - y₁) =(5/2)(x - x₁)

Lastly, you need to substitute the given point into the equation to find the equation of the line. Let

(x₁ , y₁ ) = (-2, -4)

(y - (-4)) =(5/2)(x - (-2))

y + 4 = (5/2)(x + 2)

Y + 4 = (5/2)x + 5

y = (5/2)x + 1

This is the equation of the line parallel to 5x-2y = 6 and passing through point (-2,-4)