Q59. - Algebra 2

Question

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

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

Step-by-Step Solution

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 1 – State the concept

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

Step 2 – List the given data

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

Step 3 – 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 $\left(0,\frac{8}{3}\right)$.

Step 4 – Graph the equation

Graphing the given equation using the obtained ordered pairs,