Answer:
[tex]-\dfrac{4}{3}[/tex]
Step-by-step explanation:
To find the gradient of the linear equation, 4x + 3y = 8, begin by rearranging the equation to isolate y:
[tex]4x+3y=8 \\\\\\4x+3y-4x=8-4x \\\\\\ 3y=-4x+8\\\\\\\dfrac{3y}{3}=\dfrac{-4+8}{3} \\\\\\y=-\dfrac{4}{3}x+\dfrac{8}{3}[/tex]
The equation is now in slope-intercept form, y = mx + b, where m is the slope (gradient), and b is the y-intercept.
By comparing the rearranged equation to the slope-intercept form, we can determine that the gradient (slope) of 4x + 3y = 8 is:
[tex]\LARGE\boxed{\boxed{-\dfrac{4}{3}}}[/tex]
