The equation of the line which includes points (-3 , 2) and (1 , 6) is
y = x + 5 ⇒ 2nd answer
Step-by-step explanation:
One form of the equation of a line is y = mx + b, where
- m is the slope of the line, the formula of the slope is [tex]m=\frac{y_{2}-y_{1}}{x_{2}-x_{1}}[/tex] , where [tex](x_{1},y_{1})[/tex] and [tex](x_{1},y_{1})[/tex] are two points lie on the line
- b is the y-intercept, the value of y when x = 0, to find it substitute x and y in the equation by the coordinates of any point lies on the line
∵ The line contains points (-3 , 2) and (1 , 6)
∴ [tex]x_{1}[/tex] = -3 and [tex]x_{2}[/tex] = 1
∴ [tex]y_{1}[/tex] = 2 and [tex]y_{2}[/tex] = 6
- Substitute these values in the formula of the slope above
∵ [tex]m=\frac{6-2}{1--3}=\frac{4}{4}[/tex]
∴ m = 1
∵ The form of the equation is y = mx + b
- Substitute m by 1
∴ y = x + b
- To find b substitute x and y in the equation by the coordinates
of one of the two given points
∵ [tex]x_{1}[/tex] = -3 and [tex]y_{1}[/tex] = 2
∴ 2 = -3 + b
- Add 3 to both sides
∴ 5 = b
∴ The equation of the line is y = x + 5
The equation of the line which includes points (-3 , 2) and (1 , 6) is
y = x + 5
Learn more:
You can learn more about the linear equation in brainly.com/question/8955867
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