Step-by-step explanation:
[tex]the \: gradient \: of \: line \: a \: is[/tex]
[tex]m = \frac{4}{1 } \\ m = 4[/tex]
[tex]the \: gradient \: of \: line \: b \: is[/tex]
[tex]m = \frac{ - 2}{1} \\ m = - 2[/tex]
Gradients of line A is equals to [tex]4[/tex] and gradients of line B is equals to [tex]-2[/tex].
" Gradients is defined as the ratio of difference of y-coordinates to the difference of x-coordinates."
Formula used
Gradients [tex]= \frac{y_{2}- y_{1}}{x_{2}- x_{1}}[/tex]
According to the question,
Given from the graph,
Coordinates of Line A
[tex](x_{1} ,y_{1} ) = ( 3,3)\\\\(x_{2} ,y_{2} ) = ( 4,7)[/tex]
Substitute the value in the formula we get,
Gradient of line A [tex]= \frac{7-3}{4-3}[/tex]
[tex]= 4[/tex]
Coordinates of Line B
[tex](x_{1} ,y_{1} ) = ( -1,3)\\\\(x_{2} ,y_{2} ) = ( -2,5)[/tex]
Gradient of line B [tex]= \frac{5-3}{-2-(-1)}[/tex]
[tex]= -2[/tex]
Hence, gradients of line A is equals to [tex]4[/tex] and gradients of line B is equals to [tex]-2[/tex].
Learn more about gradients here
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