Question

Can you help me with a question? What is the equation of the blue line?

Answer 1

y = - x - 1

Explanation:

the equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

calculate m using the slope formula

m =
`(y_(2)-y_(1) )/(x_(2)-x_(1) )`

with (x₁, y₁ ) = (- 1, 0) and (x₂, y₂ ) = (0, - 1) ← 2 points on the line

m =
`(-1-0)/(0-(-1))` =
`(-1)/(0+1)` =
`(-1)/(1)` = - 1

the line crosses the y- axis at (0, - 1 ) ⇒ c = - 1

y = - x - 1 ← equation of blue line

Answer 2

y = -x - 1

Explanation:

y = mx + b

slope (m): Since the line is going downhill, the slope will be negative

slope = rise / run

slope = 1 / 1

slope = 1

m = -1

y - intercept (b): this when x = 0, the line is crossing the vertical line (y-axis)

b = -1

so y = mx + b is

b = -1, m = -1

y = (-1)x + (-1)