Question

Find the equation of the line. Use exact numbers. PLEASE HELP

Answer 1

The equation of the line is y =
`-(1)/(4)` x - 6

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 =
`(y2-y1)/(x2-x1)` , 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 =
`(-7--6)/(4-0)` =
`(-7+6)/(4)` =
`(-1)/(4)`

∴ m =
`-(1)/(4)`

∵ 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 =
`-(1)/(4)` x + (-6)

∵ (+)(-) = (-)

∴ y =
`-(1)/(4)` x - 6

∴ The equation of the line is y =
`-(1)/(4)` x - 6