Question

Slope intercept form (-6,19) and (3,-2)

Answer 1

`y = -(7)/(3)x +5`

Explanation:

The general equation of a line in slope-intercept form is

y = mx + b

where m = slope and b = y-intercept is rise over run

`m = \frac {(y_(2) - y_(1))} {(x_(2) - x_(1))}`

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

For the line passing through (-6, 19) and (3, -2) , the slope

`m = (-2 - 19)/(3 - (-6))\\\\`

`\\\\m= (-21)/(9)`

`m = -(7)/(3)`

So slope-intercept form is

`y = -(7)/(3)x +b\\\\`

To compute y-intercept, b, plug in any of the two points into the above equation and solve for b

Let's choose point (3, -2)

Plugging x = 3 and y = -2 gives

`-2 = -(7)/(3)\cdot 3 +b\\\\\\\\-2 = -7 + b\\\\`

So equation of line is

`y = -(7)/(3)x +5`

Answer 2

-7/3 or -2.3

Explanation:

1. y2-y1 divided by x2-x1 which would be y2-y1/x2-x1

2. plug in : -2-19/3-(-6)

4. Solution ( -7.3 or -2.3 )