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
The line #9 x -10 y = -90# has an intersection point with the #x#-axis and an intersection point with the #y#-axis. The first point has the form #\rv{p,0}# and the second #\rv{0,q}# for certain numbers #p# and #q#. What are #p# and #q#?
#p=-10#
#q=9#
Because if #\rv{p,0}# lies on the line, then #9 p -10\cdot 0 = -90# applies (this follows from entering #x=p# and #y=0# in #9 x -10 y = -90#). This is a linear equation with unknown #p#, where #p=-10# is the solution.
Similarly, entering #x=0# and #y=q# in the equation #9 x -10 y = -90# gives the linear equation #-10\cdot q = -90# with solution #q=9#.
#q=9#
Because if #\rv{p,0}# lies on the line, then #9 p -10\cdot 0 = -90# applies (this follows from entering #x=p# and #y=0# in #9 x -10 y = -90#). This is a linear equation with unknown #p#, where #p=-10# is the solution.
Similarly, entering #x=0# and #y=q# in the equation #9 x -10 y = -90# gives the linear equation #-10\cdot q = -90# with solution #q=9#.
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