Question

Find the x-intercept and the y-intercept of the graph of each equation. Then, graph the equation.

$\mathbf{4}\mathbf{x}-\mathbf{3}\mathbf{y}+\mathbf{8}=\mathbf{0}$

Short answer

The x-intercept of the graph of the given equation is -2 and the y-intercept is $\frac{8}{3}$. The graph of the given equation is given as follows:

Step-by-step solution

– State the concept

The x-intercept is the value of x when $y=0$. Similarly, the y-intercept is the value of y when $x=0$.

– List the given data

The given equation is $4x-3y+8=0$.

– Find the intercepts

Solving for x-intercept,

$4x-3y+8=0$ (Given equation)

$4x-3\left(0\right)+8=0$ (Put $y=0$ in the given equation)

$4x+8=0$ (Simplify)

$4x+8-8=0-8$ (Subtract 8 from both sides)

$4x=-8$ (Simplify)

$\frac{4x}{4}=\frac{-8}{4}$ (Divide both sides by 4)

$x=-2$ (Simplify)

So, the x-intercept is $-2$and the graph crosses the x-axis at the point $\left(-2,0\right)$.

Similarly, solving for y-intercept,

$4x-3y+8=0$ (Given equation)

$4\left(0\right)-3y+8=0$(Put $x=0$ in the given equation)

$-3y+8=0$ (Simplify)

$-3y+8-8=0-8$ (Subtract 8 from both sides)

$-3y=-8$ (Simplify)

$\frac{-3y}{-3}=\frac{-8}{-3}$ (Divide both sides by -3)

$y=\frac{8}{3}$(Simplify)

So, the y-intercept is $\frac{8}{3}$ and thus the graph crosses the y-axis at the point $\left(0,\frac{8}{3}\right)$.

– Graph the equation

Graphing the given equation using the obtained ordered pairs,