Question

Write the equation of a line in slope intercept form that is parallel to 2X plus 4Y equals 10 and passes through the point (8,2)

Answer 1

Answer:
`y=-(1)/(2)x+6`

Explanation:

The equation of the line is slope-intercept form is:

`y=mx+b`

Where m is the slope and b thte y-intercept.

The lines are parallel, then they have the same slope.

Solve for "y" from
`2x+4y=10` to find the slopes of the lines :

`2x+4y=10\\4y=-2x+10\\y=-(1)/(2)x+(5)/(2)`

The value of the slopes of the lines is:

`m=-(1)/(2)`

Substitute the slope and the point into the equation of the line and solve for "b":

`2=-(1)/(2)(8)+b\\2=-4+b\\b=6`

Then the equation of this line is:

`y=-(1)/(2)x+6`

Answer 2

Hello!

The answer is:

The equation of the new line will be:

`y=-0.5x+6`

or

`y=-(1)/(2)x+6`

Why?

To solve the problem, we need to remember the slope intercept form of a line.

The slope intercept form of a line is given by the following equation:

`y=mx+b`

Where,

y, is the function.

x, is the variable of the function.

m, is the pendant of the line.

b, is the y-axis intercept of the line.

So, we are given the line that will be parallel to the line that we are looking for:

`2x+4y=10\\4y=-2x+10\\4y=-2(x-5)\\y=(-2)/(4)*(x-5)\\\\y=-(1)/(2)*(x-5)\\\\y=-(1)/(2)x+(5)/(2)`

Where,

`m=-(1)/(2)`

Then,

We need to use the same slope to guarantee that the new line will be parallalel to the given line-

So, our new line will have the following form:

`y=-(1)/(2)x+b`

We need to substitute the given point to isolate "b" in order to guarantee that the line will pass through.

Now, substituting the given point, to calculate"b", we have:

Calculating b, we have:

`2=-(1)/(2)8+b`

`2=-4+b`

`2+4=b`

`6=b`

Hence, we have that the equation of the new line will be:

`y=-0.5x+6`

or

`y=-(1)/(2)x+6`

Proving that the line will pass through the given point, by substituting it into its equation, we have:

`2=-0.5(8)+6`

`2=-4+6`

`2=2`

So, since the equality is satisfied, we know that the line pass through the new line.

Have a nice day!