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: $y=-\frac{1}{2}x+6$

Step-by-step 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 :

$2x+4y=10\\4y=-2x+10\\y=-\frac{1}{2}x+\frac{5}{2}$

The  value of the slopes of the lines is:

$m=-\frac{1}{2}$

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

$2=-\frac{1}{2}(8)+b\\2=-4+b\\b=6$

Then the equation of this line is:

$y=-\frac{1}{2}x+6$

Answer 2

Hello!

The answer is:

The equation of the new line will be:

$y=-0.5x+6$

or

$y=-\frac{1}{2}x+6$

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:

$2x+4y=10\\4y=-2x+10\\4y=-2(x-5)\\y=\frac{-2}{4}*(x-5)\\\\y=-\frac{1}{2}*(x-5)\\\\y=-\frac{1}{2}x+\frac{5}{2}$

Where,

$m=-\frac{1}{2}$

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:

$y=-\frac{1}{2}x+b$

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:

$2=-\frac{1}{2}8+b$

$2=-4+b$

$2+4=b$

$6=b$

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

$y=-0.5x+6$

or

$y=-\frac{1}{2}x+6$

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!