Question

Could you help me with numbers 51, 54, & 56?

Answer 1

We have to find the x-intercept and y-intercept in each equation.

The x-intercept is the value of x where the function intersects the x-axis. It corresponds to the value y=0, as that is the value of y where the x-axis is located.

The y-intercept is like the x-intercept but for the y-axis and corresponds to a value x=0.

We can see an example in a graph before solving each point:

51) We can use the fact that for the x-intercept the value of y is 0. If we replace this in the equation, we can clear the value of x that correspond to the x-intercept:

`\begin{gathered} 5x+3y=15 \\ y=0\Rightarrow5x+3\cdot0=15 \\ 5x=15 \\ x=(15)/(5) \\ x=3 \end{gathered}`

The same can be don for the y-intercept, where x=0:

`\begin{gathered} 5\cdot0+3y=15 \\ 3y=15 \\ y=(15)/(3) \\ y=5 \end{gathered}`

Then, the x-intercept is located at (3, 0) and the y-intercept is located at (0, 5).

54) We apply the same procedure as 51):

X-intercept (y=0)

`\begin{gathered} 6x+2\cdot0=8 \\ 6x=8 \\ x=(8)/(6) \\ x=(4)/(3) \end{gathered}`

Y-intercept (x=0)

`\begin{gathered} 6\cdot0+2y=8 \\ 2y=8 \\ y=(8)/(2) \\ y=4 \end{gathered}`

Then, the x-intercept is at (4/3, 0) and the y-intercept is at (0, 4).

56)

X-intercept (y=0)

`\begin{gathered} y=(2)/(3)x+1 \\ y=0\Rightarrow0=(2)/(3)x+1 \\ (2)/(3)x=-1 \\ x=-(3)/(2) \end{gathered}`

Y-intercept (x=0)

`y=(2)/(3)\cdot0+1=0+1=1`

The x-intercept is at (-3/2, 0) and the y-intercept is at (0, 1).

Answer:

51) x-intercept at (3, 0) and y-intercept at (0, 5)

54) x-intercept at (4/3, 0) and y-intercept at (0, 4)

56) x-intercept at (-3/2, 0) and y-intercept at (0, 1)