Answer: [tex]y=-\frac{1}{2}x+6[/tex]
Step-by-step explanation:
The equation of the line is slope-intercept form is:
[tex]y=mx+b[/tex]
Where m is the slope and b thte y-intercept.
The lines are parallel, then they have the same slope.
Solve for "y" from [tex]2x+4y=10[/tex] to find the slopes of the lines :
[tex]2x+4y=10\\4y=-2x+10\\y=-\frac{1}{2}x+\frac{5}{2}[/tex]
The value of the slopes of the lines is:
[tex]m=-\frac{1}{2}[/tex]
Substitute the slope and the point into the equation of the line and solve for "b":
[tex]2=-\frac{1}{2}(8)+b\\2=-4+b\\b=6[/tex]
Then the equation of this line is:
[tex]y=-\frac{1}{2}x+6[/tex]
The answer is:
The equation of the new line will be:
[tex]y=-0.5x+6[/tex]
or
[tex]y=-\frac{1}{2}x+6[/tex]
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:
[tex]y=mx+b[/tex]
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:
[tex]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}[/tex]
Where,
[tex]m=-\frac{1}{2}[/tex]
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:
[tex]y=-\frac{1}{2}x+b[/tex]
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:
[tex]2=-\frac{1}{2}8+b[/tex]
[tex]2=-4+b[/tex]
[tex]2+4=b[/tex]
[tex]6=b[/tex]
Hence, we have that the equation of the new line will be:
[tex]y=-0.5x+6[/tex]
or
[tex]y=-\frac{1}{2}x+6[/tex]
Proving that the line will pass through the given point, by substituting it into its equation, we have:
[tex]2=-0.5(8)+6[/tex]
[tex]2=-4+6[/tex]
[tex]2=2[/tex]
So, since the equality is satisfied, we know that the line pass through the new line.
Have a nice day!
