13 Write the pointslope form of the eqauation of the line sa

13.) Write the point-slope form of the eqauation of the line satisfying the conditions. Then use the point-slope form of the equation to write the slope-intercept form of the equation.

slope = -2/3, passing through (6,-2)

Solution

Point-slope form of the eqauation is y - y₁ = m (x- x₁)

Here the point = (x₁, y₁) and slope = m

(x₁, y₁) = (6, -2) and m = - 2/3

Plug the values in the form

y - (-2) = -2/3 (x - 6)

3 (y + 2) = - 2(x- 6)

3y + 6 = -2x + 12

3y = - 2x + 12 - 6

3y = - 2x + 6

Divide by 3 on both sides

y = (-2/3) x + 2 ( y = mx + b)

This is the slope-intercept form