Answer:
The equation of the line is y = [tex]-\frac{1}{4}[/tex] x - 6
Step-by-step explanation:
The 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 2 points on the line
In the given figure
∵ The line passes through points (0, -6) and (4, -7)
∴ x1 = 0 and y1 = -6
∴ x2 = 4 and y2 = -7
→ Substitute them in the rule of the slope
∵ m = [tex]\frac{-7--6}{4-0}[/tex] = [tex]\frac{-7+6}{4}[/tex] = [tex]\frac{-1}{4}[/tex]
∴ m = [tex]-\frac{1}{4}[/tex]
∵ b is the value of y at x = 0
∵ y = -6 at x = 0
∴ b = -6
→ Substitute the values of m and b in the form of the equation above
∵ y = [tex]-\frac{1}{4}[/tex] x + (-6)
∵ (+)(-) = (-)
∴ y = [tex]-\frac{1}{4}[/tex] x - 6
∴ The equation of the line is y = [tex]-\frac{1}{4}[/tex] x - 6
