Given:#" "color(brown)(4x+3y=-5)#......................(1)

#color(blue)("To find the x-intercept")#

The x-axis crosses the y-axis at #y=0# so all we need to do is substitute 0 for y and we are then able to determine x-intercept

Write equation (1) as #" "4x+3(0)=-5#

Divide both sides by 4 giving

#4/4 x=-5/4#

But #4/4 = 1#

#color(blue)(x_("intercept") =-5/4#

#color(blue)("To find the y-intercept")#

The y-axis crosses the x-axis at #x=0# so all we need to do is substitute 0 for x and we are then able to determine y-intercept

Write equation (1) as #" "4(0)+3y=-5#

Divide both sides by 3 giving

#" "3/3 y=-5/3#

But #3/3 = 1#

#" "color(blue)(y_("intercept")=-5/3)#

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#color(blue)("Drawing the graph")#

Put a mark on the x axis at #x=-5/4#

Put a mark on the y axis at #y=-5/3#

Put a ruler on the graph and draw a line that passes through both these points. Extend the line to the edges of the graph.

#color(red)("////////////////////////////////////////////////////////////////////////////")#

#color(green)("If you so wish to, this is how you change the equation into the format of")#

#" "y=mx+c#

Subtract #color(blue)(4x)# from both sides

#" "color(brown)(4xcolor(blue)(-4x)+3y=-5color(blue)(-4x)#

#" " 0+3y=-4x-5#

Divide both sides by (same as #color(blue)(xx1/3)")"#

#" "color(brown)(3ycolor(blue)(xx1/3)=(-4x-5)color(blue)(xx1/3))#

#" "3/3xx y =-4/3x-5/3#

But #3/3 =1 # giving

#" "y=-4/3x-5/3#

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