Question

What is the graph of 8x+6y=144

Answer 1

It's a linear function.

We need only two points to plotting a graph.

Convert the equation of line from the standard form to slope0intercept form.

$8x+6y=144\qquad\text{subtract 8x from both sides}\\\\6y=-8x+144\qquad\text{divide both sides by 6}\\\\y=-\dfrac{8}{6}x+\dfrac{144}{6}\\\\y=-\dfrac{4}{3}x+24$

We choose any two values of x and calculate y.

$for\ x=0\to y=-\dfrac{4}{3}(0)+24=0+24=24\to(0,\ 24)\\\\for\ x=24\to y=-\dfrac{4}{3}(24)+24=-4(8)+24=-32+24=-8\to(24,\ -8)$