Question

How do you write an equation of a line given y-intercept -8 and slope 3?

Answer 1

`y=3x-8`

I have given a detailed explanation about how it all works.

Explanation:

Consider the standard form of the equation for a strait line:

`y=mx+c`........................................(1)

Where
`m->` is the gradient (slope)
`c->color(white)(.)` is a constant (its value does not change)
`x->color(white)(.)` is a variable (can take on any value you chose)
`y->color(white)(.)` is the dependant variable (the answer)
'~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
`color(blue)("The gradient (slope)")`
`color(green)("We are told that the gradient (slope) is 3.")`

so equation (1) becomes:

`color(blue)(y=color(green)(3)x+c)`

`color(red)("This is what the graph would look like if there was no "c)`

'~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
`color(blue)("To find the value of "color(green)(c))`

Suppose we put the value of the y-intercept (given as -8) into the equation were `c` is. So equation (1) becomes

`color(blue)(y=3xcolor(green)(-8))`

`color(red)("This time the graph look like:")`

So for the equation of a strait line the `c` in the equation is the y-intercept.

Change the value of c moves the plotted line up or down

Imagine for a moment that `c= 2` then the line would cross the y-axis at y=2.

If `c=-3` then the y-intercept would be -3