Can I have some help solving this please?

[Michelle Roanoke]

It wants me to write the TWO possible point slope form equations for the the line that passes through the points (-4,12) and (-2,-4). I found one of them y-20=-8x, but what's the other one.

 

[MarkFL]

I would first determine the slope:

[MATH]m=\frac{-4-12}{-2+4}=-8[/MATH]
Now, using the first point, we may write:

[MATH]y-12=-8(x+4)[/MATH]
What do you get using the second point?

 

[ksdhart2]

I'd double check your work. Recall that if a line passes through some point \((a, b)\), that's the same as saying that if we plug in \(x = a\) and \(y = b\) to the equation of the line, we get a true statement. Let's try that now:

Does the line pass through (-4, 12)? \(x = {\color{red}-4}, \: y = {\color{blue}12} \implies {\color{blue}12} - 20 = -8({\color{red}-4}) \implies -8 = 32 \:\)

Does the line pass through (-2, -4)? \(x = {\color{red}-2}, \: y = {\color{blue}-4} \implies {\color{blue}-4} - 20 = -8({\color{red}-2}) \implies -24 = 16 \:\)

As you can see, your proposed answer results in a line that doesn't pass through either of the points. Thinking carefully about the point-slope form MarkFL showed you, and how you might manipulate it, should help you see your error and how to fix it.

 

[Michelle Roanoke]

I did what you said. I only found one equation that worked however. y=-8x-20 and I got y=-8x-34 for the second point, but that equation doesn't work when plugged back in.

 

[MarkFL]

Using the first point, I got:

[MATH]y-12=-8(x+4)[/MATH]
And using the second point:

[MATH]y+4=-8(x+2)[/MATH]
You should be able to verify that both may be written in the slope-intercept form as:

[MATH]y=-8x-20[/MATH]

 

[JeffM]

It wants me to write the TWO possible point slope form equations for the the line that passes through the points (-4,12) and (-2,-4). I found one of them y-20=-8x, but what's the other one.

I do not even understand the question. There is only one line that joins two points. What EXACTLY does the question say? (This is why our submission guidelines say to quote the actual statement of the problem completely and accurately. You have read the Submission Guidelines, I presume.)

 

[Dr.Peterson]

It wants me to write the TWO possible point slope form equations for the the line that passes through the points (-4,12) and (-2,-4). I found one of them y-20=-8x, but what's the other one.

Assuming that you almost quoted the question word for word, it is specifically asking for the two point-slope form equations, namely one obtained from each point, without simplification. Assuming that your text defines point-slope form as [MATH]y - y_1 = m(x - x_1)[/MATH], these would be [MATH]y - 12 = -8(x + 4)[/MATH] and [MATH]y + 4 = -8(x + 2)[/MATH]. These are equivalent equations, so that if they didn't specify a form, they would be one answer; if they asked for slope-intercept form, the one answer would be [MATH]y = -8x - 20[/MATH]. And your answer is none of these.