Question

How do you graph `y=3x-2` using slope intercept form?

Answer 1

See a solution process below:

Explanation:

First, this equation is in slope-intercept form. The slope-intercept form of a linear equation is: `y = color(red)(m)x + color(blue)(b)`

Where `color(red)(m)` is the slope and `color(blue)(b)` is the y-intercept value.

`y = color(red)(3)x - color(blue)(2)`

Or

`y = color(red)(3)x + color(blue)(-2)`

Therefore, we know the slope is: `color(red)(m = 3)`

And the `y`-intercept is: `color(blue)(b = -2)` or `(0, color(blue)(-2))`

We can start graphing this equation by plotting the `y`-intercept:

graph{(x^2 + (y+2)^2 - 0.025) = 0 [-10, 10, -5, 5]}

Slope is defined as `"rise"/"run"`, or the amount the `y` value changes compared to the `x` value.

The slope for this equation is `m = 3` or `m = 1`.

Therefore for each change in `y` of `3`, `x` changes by `1`.

We can now plot another point using this information:

Now, we can draw a straight line through the two points to graph the equation:

graph{(y - 3x +2)(x^2 + (y+2)^2 - 0.025)((x - 1)^2 + (y - 1)^2 - 0.025) = 0 [-10, 10, -5, 5]}