Question

How do you graph `y=3/2x-4` using the slope and intercept?

Answer 1

See a solution process below:

Explanation:

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)(3/2)x - color(blue)(4)`

Therefore:

The `y`-intercept is: `color(blue)(-4)` or `(0, color(blue)(-4))`

The slope is: `color(red)(m = 3/2)`

Slope is rise over rub. So the line will go up `3` units while it goes to the right `2` units.

We can plot the `y`-intercept as:

graph{(x^2+(y+4)^2-0.025)=0}

We can plot the next point by going up `3` units and to the right `2` units which is at: `(2, -1)`

We can now draw a line through the two points to graph the line:

graph{(x^2+(y+4)^2-0.025)((x-2)^2+(y+1)^2-0.025)(y-(3/2)x+4)=0}