Answer:
The equation of the line is y = [tex]-\frac{6}{5}[/tex] x - 2 OR 6x + 5y = -10
Step-by-step explanation:
The form of the linear equation is y = m x + b, where
- b is the y-intercept ⇒ value y at x = 0
The rule of the slope of a line is
- m = [tex]\frac{y2-y1}{x2-x1}[/tex]
- (x1, y1) and (x2, y2) are two points lie on the line
→ Let us solve the question
∵ The line passes the points (0, -2) and R (-5, 4)
∴ x1 = 0 and y1 = -2
∴ x2 = -5 and y2 = 4
→ Substitute them in the rule of the slope above to find it
∵ m = [tex]\frac{4--2}{-5-0}=\frac{4+2}{-5}=-\frac{6}{5}[/tex]
∴ m = [tex]-\frac{6}{5}[/tex]
Substitute it in the form of the equation above
∴ y = [tex]-\frac{6}{5}[/tex] x + b
∵ b is the y-intercept (value y at x = 0)
∵ At x = 0, y = -2
∴ b = -2
→ Substitute it in the equation
∴ y = [tex]-\frac{6}{5}[/tex] x + (-2)
→ Remember (+)(-) = (-)
∴ y = [tex]-\frac{6}{5}[/tex] x - 2
→ Multiply both side by 5 to cancel the denominator of the fraction
∴ 5y = -6x - 10
→ Add 6x to both sides
∴ 6x + 5y = -6x + 6x - 10
∴ 6x + 5y = -10
∴ The equation of the line is y = [tex]-\frac{6}{5}[/tex] x - 2 OR 6x + 5y = -10
