A line intersects the x-axis at -4 and has a slope of -3. Which line represents this?

[Iceycold12]

Hello.

A line intersects the x-axis at -4 and has a slope of -3. Which line represents this?

A. y=-3x+12
B. y=-3x-12
C. y=3x+4
D. y=3x-4

I gave a shot at it, and came up with this with the information given, y=-3+b (All answers had a slope of -3x/3x so I figured I'd find the y-intercept). We also have (-4,0), from the x-intercept.
I. Plug in 0 for y and -4 for x to find B
II. 0=-3(4)+b
III. 0=-12+b
IV. 12=b

I chose A. y=-3x+12.

 

[Iceycold12]

Oooh, sorry I originally put -4 on paper but was typing the problem and forgot I guess.

0=-3(-4)+b
0=12+b
-12=b

So B must be the answer then?

 

[Iceycold12]

I don't have a graphing calculator but I typed it into Google and it graphed it for me, and indeed it does cross the x-axis at -4. I tried with paper as well just in case Google was incorrect (will that ever happen?)

Just curious, the procedure to find B when line equations are in y=mx+b form, I was always told we plug in (x,y) coordinates and solve for B, which I did BUT, I didn't actually plug in x I plugged in the x-intercept of -4, so are they synonyms, x and x-intercept?

 

[Iceycold12]

I think I understand, only when y=0 is when an x-intercept can be used in place of x. Thank you

 

[Iceycold12]

I see, thanks. So when given an x point AND a x-intercept and y point, I would x and y, because the x-intercept is simply part of the function/line?

 

[Iceycold12]

You seem to be floating around very close to getting this firmly in your mind without ever quite getting there. If you look at it, you will see that you have not even written a coherent sentence. This sentence no verb. Let's review some basics.

The notation for indicating a point in the x-y plane is (x, y) because x comes before y alphabetically. You know that. Just reminding you about basics.

A linear equation has the algebraic form y = ax + b. The parameter a is called the slope, and the parameter b is called the y-intercept.

The graph of a linear equation is a straight line.

"The y-intercept is b" is just another way to say that the point (0, b) is on the line graphing the equation. It is the point where the line cuts, intersects, intercepts the y-axis. The word 'intercept' is just a way to identify a specific point. DO NOT THINK THAT INTERCEPT IS ANYTHING BUT A POINT. An intercept is a point with the special property that one of the two numbers describing the point is 0. Now what seems a bit confusing is that it is x that is 0 at the y-intercept. That is not strange once you remember that the y-intercept is where the graph cuts the y-axis, and x = 0 all along the y-axis.

Similarly, the x-intercept is w" is just another to say that the point (w, 0) is on the line graphing the equation.

Two points UNIQUELY determine a straight line. Usually the quickest way to graph a linear equation is to calculate the x-intercept and the y-intercept and draw the line between those two points. AN INTERCEPT IS A POINT; THAT IS, IT IS A PAIR OF NUMBERS. But only one number is given because the other one is zero.

Got it now?

Yes, got it now, thanks a lot.