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 #7 x -8 y = -56# 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=-8#
#q=7#
Because if #(p,0)# lies on the line, then #7 p -8\cdot 0 = -56# applies (this follows from entering #x=p# and #y=0# in #7 x -8 y = -56#). This is a linear equation with unknown #p#, where #p=-8# is the solution.
Similarly, entering #x=0# and #y=q# in the equation #7 x -8 y = -56# gives the linear equation #-8\cdot q = -56# with solution #q=7#.
#q=7#
Because if #(p,0)# lies on the line, then #7 p -8\cdot 0 = -56# applies (this follows from entering #x=p# and #y=0# in #7 x -8 y = -56#). This is a linear equation with unknown #p#, where #p=-8# is the solution.
Similarly, entering #x=0# and #y=q# in the equation #7 x -8 y = -56# gives the linear equation #-8\cdot q = -56# with solution #q=7#.
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