To find the #x#-intercept, set #y# to #0# and solve for #x#:
#8x + 5y = -10# becomes:
#8x + (5 * 0) = -10#
#8x + 0 = -10#
#8x = -10#
#(8x)/color(red)(8) = -10/color(red)(8)#
#(color(red)(cancel(color(black)(8)))x)/cancel(color(red)(8)) = -5/4#
#x = -5/4# or #(-5/4, 0)#
Another way to find this solution is to use the fact this equation is in Standard Linear form.
The standard form of a linear equation is: #color(red)(A)x + color(blue)(B)y = color(green)(C)#
Where, if at all possible, #color(red)(A)#, #color(blue)(B)#, and #color(green)(C)#are integers, and A is non-negative, and, A, B, and C have no common factors other than 1
#color(red)(6)x + color(blue)(5)y = color(green)(-10)#
The #x#-intercept of an equation in standard form is: #color(red)(A)/color(blue)(B)#
#color(red)(8)/color(blue)(-10) = -5/4# or #(-5/4, 0)#
