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Question

write down the equations of the lines that are parallel to:

 

 

a) 2y=5x+7, passing through (0,-3.5)

 

b) 7x+6y=13, passing through (6,7) 

 

thanks!

 

 

Answer 1

Hi Rei,

 

 

   write down the equations of the lines that are parallel to:


a) 2y=5x+7, passing through (0,-3.5)

 

Parallel lines have the same slope.       2y=5x+7

 Divide each term by 2:                       y=5/2x+7/2

 

The slope is 5/2.

Now we need to find an equation that goes through point (0,-3.5)

Use slope-intercept form:   y=mx+b

                                       y=5/2x+b

Substitute in the point:    -3.5=5/2(0)+b

                                      -3.5=b

 

ANSWER:  The equation is   y=5/2x-3.5  or y=2.5x-3.5

 

 

b) 7x+6y=13, passing through (6,7) 

 

 

This equation is in standard form Ax+By=C

The slope is -A/B =-7/6

Use slope-intercept form to find the y-intercept:

                                               y=mx+b

                                               y=-7/6x+b

substitute in the point:              7=(-7/6)(6)+b

                                               7=-7 +b

add 7 to both sides:                  14=b

 

ANSWER:  y=-7/6x+14              It is best to leave -7/6 as a fraction because it is a repeating decimal.  When 

                                                a repeating decimal is rounded the answer in not considered to be exact.

 

Hope this helps you understand the process.