Question

How do you graph using the intercepts for `y=-6x-9`?

Answer 1

See a solution process below:

Explanation:

Because this equation is in slope-intercept form we can find the `x`-intercept and `y`-intercept directly from the equation. The slope-intercept form of a linear equation is: `y = color(red)(m)x + color(blue)(b)`

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

`y = color(red)(-6)x - color(blue)(9)`

Therefore the `y`-intercept is: `color(blue)(b = -9)` or `(0, color(blue)(-9))`

And, the `x`-intercept is:

`color(blue)(- -9)/color(red)(-6) => color(blue)(9)/color(red)(-6) => -color(blue)(3 xx 3)/color(red)(3 xx 2) => -color(blue)(color(black)(cancel(color(blue)(3))) xx 3)/color(red)(color(black)(cancel(color(red)(3))) xx 2) => -3/2`

Or

#(-3/2, 0)

We can next plot the two points on the coordinate plane:

graph{(x^2+(y+9)^2-0.3)((x+ 3/2)^2+y^2-0.3)=0 [-30, 30, -15, 15]}

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

graph{(y+6x+9)(x^2+(y+9)^2-0.3)((x+ 3/2)^2+y^2-0.3)=0 [-30, 30, -15, 15]}