Answer:
1) The equation of the line is y = [tex]\frac{-1}{2}[/tex] x + 4
2) The equation of the line is y = -12x + 8
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, m = Δy/Δx (chang of y/change of x)
- b is the y-intercept (value y at x = 0)
Let us solve the two questions
1)
∵ points (-2, 5) and (2, 3) lie on the same line
→ Find the slope m
∵ Δ x = 2 - (-2) = 2 + 2 = 4
∵ Δ y = 3 - 5 = -2
∴ m = [tex]\frac{-2}{4}=\frac{-1}{2}[/tex]
∴ The slope of the line is [tex]\frac{-1}{2}[/tex]
→ Substitute the value of m in the form of the equation above
∴ y = [tex]\frac{-1}{2}[/tex] x + b
→ To find b substitute the x and y in the equation by the coordinates
of a point on the line
∵ Point (-2, 5) lies on the line
∴ x = -2 and y = 5
∵ 5 = [tex]\frac{-1}{2}[/tex](-2) + b
∴ 5 = 1 + b
- Subtract 1 from both sides
∴ 5 - 1 = 1 - 1 + b
∴ 4 = b
→ Sustitute it in the equation
∴ y = [tex]\frac{-1}{2}[/tex] x + 4
The equation of the line is y = [tex]\frac{-1}{2}[/tex] x + 4
2)
∵ The slope of the line is -12
∴ m = -12
∵ The line passes through point (0, 8)
∵ b is the value of y at x = 0
∴ b = 8
→ Substitute the values of m and b in the form of the equation above
∴ y = -12x + 8
The equation of the line is y = -12x + 8
