If l is the line through the point (-3,5) having a slope of 2/3 . complete the equation of l y = a.(2/3)x + 7 b. (2/3)x + (47/9) c. (2/3)x - (1/3) and explain briefly pls

point slope form  (y-y1) = m(x-x1)

y-5=(2/3)(x-(-3))

y-5=(2/3)(x+3)                    add 5 to each side and distribute

y= 2/3x +2/3 *3 +5

y = (2/3)x +2 +5  

y = (2/3) + 7                        

step-by-step explanation:

5x + 3y = - 4

step-by-step explanation:

the equation of a line in standard form is

ax + by = c ( a is a positive integer and b, c are integers )

express the line first of all in slope- intercept form

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

to calculate m use the gradient formula

m = ( y₂ - y₁ ) / ( x₂ - x₁ )

with (x₁, y₁ ) = (7, - 3) and (x₂, y₂ ) = (4, - 8)

m = = -

y = - x + c ← is the partial equation

to find c substitute either of the 2 points into the partial equation

using (4, - 8 ), then

- 8 = - + c ⇒ c = -

y = - x - ← in slope-intercept form

multiply all terms by 3 to eliminate the fractions

3y = - 5x - 4 ( add 5x to both sides )

5x + 3y = - 4 ← in standard form