Question

48. Find the x– and y–intercepts of the line: 3x + 4y = –24.A. 3, 4B. 8, 6C. –8, –6D. –3, –4

Answer 1

C. –8, –6

Explanation:

Given the equation:

`3x+4y=-24`

(a)x-intercept

The x-intercept is the value of x at which y=0.

When y=0:

`\begin{gathered} 3x+4y=-24 \\ 3x+4(0)=-24 \\ 3x=-24 \\ \text{Divide both sides y 3} \\ \implies x=-(24)/(3) \\ x=-8 \end{gathered}`

b)y-intercept

The y-intercept is the value of y at which x=0.

When x=0:

`\begin{gathered} 3x+4y=-24 \\ 3(0)+4y=-24 \\ 4y=-24 \\ \text{Divide both sides by 4} \\ \implies y=-(24)/(4) \\ y=-6 \end{gathered}`

The x– and y–intercepts of the line: 3x + 4y = –24 are –8 and –6.

Option C is correct.