Mathematics, 09.10.2019 08:30 teacherpreacher

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)

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Answer from: angoraspinner

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

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 from: TordtheMan982

Hello!

The answer is:

The equation of the new line will be:

y=-0.5x+6

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

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

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

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!

Answer from: Quest

300pi

step-by-step explanation:

Answer from: Quest

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