Question

What is the gradient of the graph shown?Give your answer in its simplest form.

Answer 1

gradient = 1

Explanation:

calculate the gradient using the slope formula

m =
`(y_(2)-y_(1) )/(x_(2)-x_(1) )`

with (x₁, y₁ ) = (0, - 2) and (x₂, y₂ ) = (2, 0) ← 2 points on the line

m =
`(0-(-2))/(2-0)` =
`(0+2)/(2)` =
`(2)/(2)` = 1

Answer 2

`\underline{\underline{\large\bf{Solution:-}}}\\`

`\longrightarrow`By observing the graph of the line , we can observes that it intersects x- axis at 2 and y -axis at -2 i.e., it passes through (2,0) and (0,-2) respectively.

`\textsf{The gradient of a line passing through two}`
`\sf{given \: points \:(x_1,y_1) \:and \:(x_2,y_2) \: is \:given \: by - }`

`\green{ \underline { \boxed{ \sf{ Gradient =(y_2-y_1)/(x_2-x_1)}}}}`

Here,

• 
  `\sf{x_1= 2}`
• 
  `\sf{y_1=0}`
• 
  `\sf{x_2=0}`
• 
  `\sf{y_2= -2}`

Putting Values:-

`\begin{gathered}\\\implies\quad \bf Gradient =(-2-0)/(0-2) \\\end{gathered}`

`\begin{gathered}\\\implies\quad \bf \frac{\cancel{-2}}{\cancel{-2}} \\\end{gathered}`

`\begin{gathered}\\\implies\quad \bf 1 \\\end{gathered}`

>>The gradient of the graph shown is 1