Suppose that I give that a line passes thru (-4,6) and parallel to the line y= 1/4 x+10. Find the eq of the new line."

Question

Suppose that I give that a line passes thru (-4,6) and parallel to the line y= 1/4 x+10. Find the eq of the new line." Step by step. Please answer the question in English with no variables. Also, how about if you add a CHECK line after calculating both variable show that both equations are true after you substitute both values in.

 

Answer 1

Parallel lines have the same slope.

 

You start with y = mx + b and since the slope you need is 1/4, that gives you m, so you now have y = (1/4)x + b.

 

This equation has to work for the point (-4,6), so you can input x = 4 and y = 6 from the point and that gives you an equation where only b is missing.  Then you solve for b. 

 

Now fill in the 1/4 for m and the value you get for b into y = mx + b and that is the answer to the question. 

 

Alternatively, if you remember the point-slope equation for a line, you can plug in the values from the point and the slope all at once and simplify the result down to y = mx + b and you'll get the same answer.