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

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

I'm not exactly sure how explain this without variables, but...

 

This problem is solved using the point-intercept form of the line. You plug in the point and slope into the formula, then simplify until your equation resembles slope-intercept form. 

 

Point-intercept form: (y-y₀)=m(x-x₀), with m representing the slope of the line. 

A line parallel to the given line would have a slope equal to the given slope, so m=(1/4).

 

Assuming (-4,6)=(x₀,y₀) and plugging it and the slope into the formula,

 

(y-6)=(1/4)(x-(-4))

(y-6)=(1/4)(x+4)

(y-6)=(1/4)x+1

 

Now, rearranging to resemble slope-intercept form:

 

y-6=(1/4)x+1

y=(1/4)x+7

 

Now, to check, plug the x and y value of the point into the new equation you've created, and it should work out. 

 

y=(1/4)x+7

6=(1/4)(-4)+7

6=-1+7

6=6