Question

Which equation best represents the line? (4 points)

a
y = 1 over 3.x − 1

b
y = 3x − 1

c
y = −x + 1 over 3.

d
y = 3x + 1

Answer 1

The equation of the line is y = 3x - 1 ⇒ b

Explanation:

From the given graph

∵ The rule of the slope of the line is m =
`(y2-y1)/(x2-x1)`

∵ (x1, y1) and (x2, y2) are two points on the line

∵ The line passes through points (0, -1) and (1, 2)

∴ x1 = 0 and y1 = -1

∴ x2 = 1 and y2 = 2

→ Substitute them in the rule of the slope to find it.

∵ m =
`(2--1)/(1-0)` =
`(2+1)/(1)` =
`(3)/(1)`

∴ m = 3

∵ The line intersects the y-axis at point (0, -1)

∴ The y-intercept = -1

∵ The form of the equation of the line is y = m x + b

∵ b is the y-intercept

∴ b = -1

→ Substitute the values of m and b in the form of the equation

∵ y = 3x + -1

∴ y = 3x - 1

∴ The equation of the line is y = 3x - 1