Question

Lines a and b are parallel. Line a is described by the equation 3x - 7y = 21. Line b passes

Answer 1

Answer:  The equation   3x - 7y = -27    or 7y = 3x +27  represents line b

y = ³/₇x +  ²⁷/₇  also represents line b using originally calculated fractions.

The attachment shows the graphs of the lines.

Step-by-step explanation:

I find it easier to work with equations in slope-intercept form, y = mx + b, so the equation 3x -7y = 21 becomes -7y = -3x + 21  then y = 3/7 x - 3

Substitute the values of the coordinate given (-2,3) for y and x in the equation and solve for b.

3 = 3/7(-2) + b

3 = -6/7 + b  Add  6/7 to both sides

3 + 6/7 = b   You can leave 3⁶/₇ as the slope or chamge toan improper fraction

²⁷/₇ = b

Rewrite the equation with the original slope and the calculated value of b

y = ³/₇x -  ²⁷/₇

as both denominators are 7, the equation can be simplified to

7y = 3x +27 or to standard form

3x - 7y = -27