Question

Find and graph the intercepts of the following linear equation:5x-2y=-10

Answer 1

x-intercept = -2

y-intercept = 5

Step-by-step explanation:
`\begin{gathered} Given: \\ 5x\text{ - 2y = -10} \end{gathered}`

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

To get the x-intercept, we will substitute y with zero:

`\begin{gathered} 5x\text{ - 2\lparen0\rparen = -10} \\ 5x\text{ = -10} \\ divide\text{ both sides by 5:} \\ x\text{ = -10/5} \\ \text{x = -2} \\ So,\text{ the x-intercept = -2} \end{gathered}`

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

To get the y-intercept, we will substitute x with zero:

`\begin{gathered} 5(0)\text{ - 2y = -10} \\ -2y\text{ = -10} \\ divide\text{ both sides by -2:} \\ (-2y)/(-2)\text{ = }(-10)/(-2) \\ division\text{ of same signs give positive sign} \\ y\text{ = 5} \\ So,\text{ the y-intercept = 5} \end{gathered}`

Plotting the graph: