write the equation of a line parallel to the given y=-1/2x+1;(4,2)

Question

but passing through the given point.

Answer 1

Hello, thank you for taking the time to post your question!

The general form that you want to operate under here is slope-intercept form, meaning y = mx + b. since the lines are parallel you can just pull the slope out of the other equation directly … m = -1/2

From there then we can use the equation to solve for the y-intercept for the new line

y = -1/2x + b

2 = -1/2(4) + b

2 = -2 + b

4 = b

Putting it all together then the final equation for the new line is y = -1/2x + 4

I hope that helps get you moving in the right direction! Feel free to reach out if you have any additional questions beyond that :)

Answer 2

If two lines are parallel, the slopes are equal.  The equation is written in slope y-intercept form, y = mx + b, where m = the slope and b = the y-intercept.

 

So the slope of the line, and therefore, its parallel, is 1/2.

 

So the equation of the new line is y = 1/2x + b.  To find the value of b, use the point (4, 2). 

 

That makes the equation 2 = 1/2(4) + b, so 2 = 2 + b.  Solving this, b = 0.

 

The final equation is:  y = 1/2x + 0, or y = 1/2x.