how to find the slope from point slope form

Question

I am doing homework and the problem says to find the equation that passes through a point but it only gives one point and o slope.

Answer 1

Anytime the slope (commonly called "m") is 0, that means that the line is not sloping up or sloping down.  It's just a "flat" line (think heart rate monitor and bad news).

 

Whatever the y-value is will be the equation of that line, or generically y=b.

 

For example, I could have a line with a slope of 0 that also happened to go through (3, 5).

Because it's horizontal, it will also go through (2, 5) and (1, 5) and (0, 5) and (4, 5) and we could go on and on and also add decimals to the list, such as (3.5, 5).

 

You've probably heard that when x=0, that point's y-value is the y-intercept (commonly referred to as "b").

 

So, in my example, if I were to use the slope-intercept form of a line to find an equation:

y = mx + b

y = 0x  + 5

y = 5

 

Point-slope works, too, but my students have sometimes asked for a faster way to know more...

If m=0, it's horizontal.

If it's horizontal, it will hit or intersect the y-axis. (It *might* also be the x-axis, but that's rare.)

If it hits an axis in a countable number of places (not an infinte number, like an entire axis), then that axis will be named in the equation. If it doesn't hit in a specific point(s), it won't be named at all.

Horizontal lines hit the y-axis in a specific point, so y will be named in the equation.

y=? (Look at the ordered pair and use the y-value.)

Answer 2

If the slope is 0, the line is horizontal and parallel to the x-axis.

The point-slope form is y-y₁=m(x-x₁) for the point (x₁,y₁).

For example, use the point (2,3).

y-3=0(x-2)

y-3=0

y=3 is the equation of the line. This line is a horizontal line that is parallel to the x-axis and goes through all points of the form (x,3). This line is perpendicular to the y-axis and x can be any number but y will always be 3.