Question

Find the y-intercept and x-intercept of the following linear equation3X-576Answer* KeypadKeyboard ShortcutsEnter the coordinates to plot points on the graph. Any lines or curves will be drawn once all required pointsare plotted.1015y-intercept (A):X105510x-intercept (B):(5-19

Answer 1

Y-intercept A: (0, -8.4)

X-intercept B: (8, 0)

Step-by-step explanation:
`\begin{gathered} Given: \\ (3)/(4)x\text{ -}(5)/(7)y\text{ = 6} \end{gathered}`

x-intercept is the value of x when y = 0

To get the x-intercept of the equation, we will substitute y with 0:

`\begin{gathered} (3)/(4)x\text{ - }(5)/(7)\left(0\right)\text{ = 6} \\ (3)/(4)x\text{ - 0 = 6} \\ (3)/(4)x\text{ = 6} \\ multiply\text{ through by 4:} \\ 3x\text{ = 6\lparen4\rparen} \end{gathered}`
`\begin{gathered} 3x\text{ = 24} \\ divide\text{ both sides by 3:} \\ (3x)/(3)\text{ = }(24)/(3) \\ x\text{ = 8} \end{gathered}`

x-intercept = 8

In ordered pair: (8, 0)

y-intercept is the value of y when x = 0

To get the y-intercept of the equation, we will susbtitute x with 0:

`\begin{gathered} (3)/(4)\left(0\right)\text{ - }(5)/(7)y\text{ = 6} \\ 0\text{ - }(5)/(7)y\text{ = 6} \\ -(5)/(7)y\text{ = 6} \\ multiply\text{ through by 7:} \\ -5y\text{ = 6\lparen7\rparen} \end{gathered}`
`\begin{gathered} -5y\text{ = 42} \\ divide\text{ both sides by -5:} \\ y\text{ = 42/-5} \\ y\text{ = -8.4} \end{gathered}`

y-intercept = -8.4

In ordered pair: (0, -8.4)

Y-intercept A: (0, -8.4)

X-intercept B: (8, 0)