Answer:
The equation of the line in slope-intercept form is y = -x + 6
Step-by-step explanation:
The form of the slope-intercept form of the linear equation is
y = m x + b, where
- m is the slope of the line
The rule of the slope is [tex]m=\frac{y2-y1}{x2-x1}[/tex] , where
- (x1, y1) and (x2, y2) are two points on the line
Let us choose two points on the line to form the equation
∵ Points (6, 0) and (0, 6) lie on the line
∴ x1 = 6 and y1 = 0
∴ x2 = 0 and y2 = 6
→ Substitute them in the rule of the slope to find it
∵ [tex]m=\frac{6-0}{0-6}=\frac{6}{-6}=-1[/tex]
∴ m = -1
→ Substitute it in the form of the equation above
∵ y = -1(x) + b
∴ y = -x + b
∵ b is the y-intercept
∵ The y-intercept is the value of y at x = 0
∵ At x = 0, y = 6
∴ b = 6
→ Substitute the value of b in the equation
∵ y = -x + 6
∴ The equation of the line in slope-intercept form is y = -x + 6
