Question

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 ​

Answer 1

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 = -
`(1)/(2)`x + 3

b.) 3x - 2y + 12 = 0

-2y = -3x - 12

y =
`(3)/(2)`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 = -
`(1)/(2)`, meaning -
`(1)/(2)` is the slope, and b = 3, meaning the y-intercept is 3.

In the second equation, the m =
`(3)/(2)`, meaning
`(3)/(2)` is the slope, and b = 6, meaning the y-intercept is 6.

Hope this helps! :)