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)

Step-by-step explanation:

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

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

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

Solve for "y"  from   to find the slopes of the lines :

The  value of the slopes of the lines is:

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

Then the equation of this line is:

The answer is:

The equation of the new line will be:

or

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:

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:

Where,

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:

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:

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

or

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

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

Have a nice day!

step-by-step explanation:

f(x)=2x^2 -1 

translation is a function transformation that transform the function in a way of translating. by translating the function its graph is moved  up an down. moving the function f(x) 2 units to the left will be the new function g(x) with the equation: g(x)=f(x+2)=2(x+2)^2 -1

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step-by-step explanation: