I am having real trouble with Slope - Intercept should "m" always be a fraction? Or a whole number?

Question

Slope - Intercept 

Graphing points

Answer 1

The slope of a line is often referred to as "rise over run."  That means:

              (the increase in the y-value) / (the increase in the x-value)

 

So, for a horizontal line, the slope is 0.

 

For the line y=x (this is 45°), the slope is 1.

 

For lines between a horizontal line (y=constant) and y=x, the slope is some fraction between 0 and 1.

 

Between y=x and a vertical line, the slope increases rapidly.  If a line goes thru the Origin (0,0) and the point (1,1000), it has a slope of 1000.  A vertical line has an undefined slope (because the run cannot be zero).

 

Lines that decrease y-values as x-values increase have negative slope.  So, y=-x has a slope of (-1).  A very important note here is that perpendicular lines (lines that intersect with a 90° angle) have slopes that are the negative reciprocal of each other -- if the slope of a line is m, then the perpendicular line has slope (-1/m).

 

The slope-intercept form of the equation of a line is:  y=mx+b

That means that if x increases by 1, then y increases by m.          [remember, "rise over run"]

 

For the Standard Form of the equation of a line (Ax+By=C), the slope is (-A/B).

 

We use words like "flat," "level," "plane" and ""steep," "upright," "straight up/down" to express slope.

Answer 2

The slope (m) can be literally any value. 1, 2, 3, 1.3, 0.4, 1/6, 7/8, -3/45, etc.

 

A few examples...

 

y = 2x + 3.5                 the slope is 2, y intercept is 3.5

 

y = (1/4)x - 6               the slope is (1/4), y intercept is -6

 

y = 5.645x + 8.6          the slope is 5.645, y intercept is 8.6

 

For all these equations, the b (y-intercept) is the number that is added or subtracted at the end. The logic behind this is that the line hits the y-axis when x = 0. So, plug x=0 into any of these equations. Anything multiplied by 0 is equal to 0, so we're left with just the number that doesn't have an x attached to it.

 

I hope this helps!