hello! it would be much appreciated if someone could show me the steps of how to change from standard form to y intercept form and also explain how I can determine the slope and y intercept in the 2nd question ​

Standard Form:Ax + By = Cy-intercept Form:y = mx + bChanging from Standard to y-intercept:When you are given an equation in standard form, you are provided with the coefficients for the x and y variables, along with a constant. The first thing we should do is isolate the y variable, as y-intercept form has only a y variable on one side. This can be done like so (using part A as an example):     5x - y + 3 = 0             (Original equation)     -y = -5x - 3            Subtract 3 and 5x from both sides.     y = 5x + 3             Divide both sides by the coefficient of the y variable.As you can see, the equation now is in y-intercept form.Determining the Slope and y-intercept:For your case, the easiest (and intended) way of finding the slope and y-intercept is to convert the 2 given equations into y-intercept form. Do the same thing we did previously:a.) x + 2y - 6 = 0     2y = -x + 6     y = -[tex]\frac{1}{2}[/tex]x + 3b.) 3x - 2y + 12 = 0     -2y = -3x - 12      y = [tex]\frac{3}{2}[/tex]x + 6From here, it's just a matter of extracting the information from the 2 equations. Recall that y-intercept form isy = mx + b     where b is the y-intercept     and m is the slope.In the first equation, the m = -[tex]\frac{1}{2}[/tex], meaning -[tex]\frac{1}{2}[/tex] is the slope, and b = 3, meaning the y-intercept is 3.In the second equation, the m = [tex]\frac{3}{2}[/tex], meaning [tex]\frac{3}{2}[/tex] is the slope, and b = 6, meaning the y-intercept is 6.Hope this helps! :)