Answer:

Slope-Intercept Form states that in the equation of a straight line y=mx+b the slope is the number represented by m that is multiplied on the x, and b is the y intercept i.,e the point where line cut the vertical  y-axis.

Given equation: 5x+2y=3              ……[1]

To convert this equation into slope intercept form;

Subtraction Property of equality states that you subtract the same number from both sides of an equation.

Subtract 5x from both sides in equation [1];

5x+2y-5x=3-5x

Simplify:

2y=3-5x or we can write this as;

2y=-5x+3                 ……[2]

Division property of equality states that you divide the same number from both sides of an equation:

Divide by 2 from both sides of an equation in [2]

frac{2y}{2} =frac{-5x+3}{2}

On simplify:

y=-frac{5}{2}x+frac{3}{2}

Therefore, the given equation in slope intercept form is: y=-frac{5}{2}x +frac{3}{2}