The equation of the line containing the given pair of points (4.6 , -8) and (6.6 , 2.2) is y = 5.1 x - 31.46
Step-by-step explanation:
The equation of a line is y = m x + b, where
∵ The line contains the points (4.6 , -8) and (6.6 , 2.2)
∴ [tex]x_{1}[/tex] = 4.6 and [tex]x_{2}[/tex] = 6.6
∴ [tex]y_{1}[/tex] = -8 and [tex]y_{2}[/tex] = 2.2
∵ [tex]m=\frac{y_{2}-y_{1}}{x_{2}-x_{1}}[/tex]
- Substitute the values above in the rule of m
∴ [tex]m=\frac{2.2-(-8)}{6.6-4.6}=\frac{2.2+8}{2}=\frac{10.2}{2}=5.1[/tex]
∴ The slope of the line is 5.1
∵ The equation of a line is y = m x + b
Substitute m by 5.1
∴ y = 5.1 x + b
To find b substitute x and y by the coordinates of point (4.6 , -8) OR point (6.6 , 2.2)
∵ x = 6.6 and y = 2.2
∴ 2.2 = 5.1(6.6) + b
∴ 2.2 = 33.66 + b
- Subtract 33.66 from both sides
∴ -31.46 = b
∴ y = 5.1 x + (-31.46)
∴ y = 5.1 x - 31.46
The equation of the line containing the given pair of points (4.6 , -8) and (6.6 , 2.2) is y = 5.1 x - 31.46
Learn more:
You can learn more about the linear equation in brainly.com/question/1284310
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