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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