### Linear formulas and equations: Linear equations and inequalities

### Intersection points of linear formulas with the axes

Intersection point with the x-axis

Intersection point with the y-axis

On the line #4 x -7 y = -28# there is point of the #x#-axis and a point of the #y#-axis. The first point has the form #(p,0)# and the second #(0,q)# for certain numbers #p# and #q#. What are #p# and #q#?

#p=-7#

#q=4#

Because if #(p,0)# lies on the line, then #4 p -7\cdot 0 = -28# applies (this follows from entering #x=p# and #y=0# in #4 x -7 y = -28#). This is a

Similarly, entering #x=0# and #y=q# in the equation #4 x -7 y = -28# gives the linear equation #-7\cdot q = -28# with solution #q=4#.

#q=4#

Because if #(p,0)# lies on the line, then #4 p -7\cdot 0 = -28# applies (this follows from entering #x=p# and #y=0# in #4 x -7 y = -28#). This is a

*linear equation*with unknown #p#, where #p=-7# is the solution.Similarly, entering #x=0# and #y=q# in the equation #4 x -7 y = -28# gives the linear equation #-7\cdot q = -28# with solution #q=4#.

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