Answer: y = - x - 6
Explanation:
The equation of a straight line can be represented in the slope-intercept form, y = mx + c
Where c = intercept
Slope, m = change in value of y on the vertical axis / change in value of x on the horizontal axis
change in the value of y = y2 - y1
Change in value of x = x2 -x1
y2 = final value of y
y 1 = initial value of y
x2 = final value of x
x1 = initial value of x
The line passes through (3,-9) and (4,- 10)
y2 = - 10
y1 = - 9
x2 = 4
x1 = 3
Slope,m = (- 10 - - 9)/(4 - 3) = - 1/1 = - 1
To determine the intercept, we would substitute x = 4, y = - 10 and m = - 1 into y = mx + c. It becomes
- 10 = - 1 × 4 + c
- 10 = - 4 + c
c = - 10 + 4
c = - 6
The equation becomes
y = -x - 6