Standard Form:
Ax + By = C
y-intercept Form:
y = mx + b
Changing 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 + 3
b.) 3x - 2y + 12 = 0
-2y = -3x - 12
y = [tex]\frac{3}{2}[/tex]x + 6
From here, it's just a matter of extracting the information from the 2 equations. Recall that y-intercept form is
y = 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! :)
