Question

choose the x-intercept and the y-intercept for the equation 2x+5y=14a (-7,0)b (0,5/14)c (0,14/5)d) (0,7)e (7,0)

Answer 1

Given: The equation below

`2x+5y=14`

To Determine: The x-intercept and the y-intercept of the equation

Solution

The x-intercept is the point where the graph of the linear function cuts the x-axis. At the x-intercept, the coordinate of y is 0 (i.e. y = 0)

The y-intercept is the point where the graph of of the linear function cuts the y-axis. At the y-intercept, the coordinate of x is 0 (i.e. x = 0)

To find y-intercept, make x = 0

`\begin{gathered} 2x+5y=14 \\ 2(0)+5y=14 \\ 5y=14 \\ y=(14)/(5) \end{gathered}`

To find x-intercept, make y = 0

`\begin{gathered} 2x+5y=14 \\ 2x=5(0)=14 \\ 2x=14 \\ x=(14)/(2) \\ x=7 \end{gathered}`

Hence, the coordinate of the y - intercept is (0, 14/5), OPTION C, and the coordinate of the x-intercept is (7, 0), OPTION E