Question

write the equation of a line given the following information: passes through the points (-4,-5) and (6,0)

Answer 1

To write the equation for a line, we need to know only two things, the slope and the y-intercept.

We can figure the slope out by using "Rise over Run", which is where you take two points on a line, and measure how far the line goes up (rises) and how far the line goes to the right (runs) between the two points.

Your points are (-4,-5) and (6,0), so the "Rise" would be how far the line goes up between 0 and -5, which is obviously 5. The "Run" would be how far the line goes to right between -4 and 6, which is 10.

So using "Rise over Run", the slope would be 5/10, or 1/2.

We now need to find the y-intercept. We can do this by using the point-slope equation. (Which is the equation for a line when you only know one point, and the slope):

\[y-y _{1}=m(x-x _{1})\]
where m is the slope and x and y with a little one under them are a specific point on the line.

We know that m = 1/2 and we have the point (6,0) so we plug that into the equation to get

\[y-0=(1/2)(x-6)\]
which simplifies to
\[y=(1/2)x -3\]

And that is our equation for the line!

Answer 2

thank you so much!