Answer:
The equation that represented by the line is y = -x + 2
Step-by-step explanation:
The slope-intercept form of the linear equation is y = m x + b, where
- m is the slope of the line
- b is the y-intercept (value y at x = 0)
The rule of the slope is m = [tex]\frac{y2-y1}{x2-x1}[/tex] , where
- (x1, y1) and (x2, y2) are two points on the line
From the given figure
∵ The line passes through points (2, 0) and (0, 2)
∴ x1 = 2 and y1 = 0
∴ x2 = 0 and y2 = 2
→ Substitute them in the rule of the slope to find it
∵ m = [tex]\frac{2-0}{0-2}=\frac{2}{-2}=-1[/tex]
∴ m = -1
→ Substitute it in the form of the equation above
∵ y = -1(x) + b
∴ y = -x + b
∵ b is value y at x = 0
∵ At x = 0, y = 2
∴ b = 2
→ Substitute it in the equation above
∴ y = -x + 2
∴ The equation that represented by the line is y = -x + 2
