2. The Straight Line
Slope-Intercept Form of a Straight Line
The slope-intercept form (otherwise known as "gradient, y-intercept" form) of a line is given by:
y = mx + b
This tells us the slope of the line is m and the y-intercept of the line is b.
The line y = 2x + 4 has
- slope `m = 2` and
- y-intercept `b = 4`.
We do not need to set up a table of values to sketch this line. Starting at the y-intercept (`y = 4`), we sketch our line by going up `2` units for each unit we go to the right (since the slope is `2` in this example).
To find the x-intercept, we let `y = 0`.
2x + 4 = 0
`x = -2`
We notice that this is a function. That is, each value of x that we have gives one corresponding value of y.
See more on Functions and Graphs.
Point-Slope Form of a Straight Line
We need other forms of the straight line as well. A useful form is the point-slope form (or point - gradient form). We use this form when we need to find the equation of a line passing through a point (x1, y1) with slope m:
y − y1 = m(x − x1)
Find the equation
of the line that passes through `(-2, 1)` with slope of `-3`.
General Form of a Straight Line
Need Graph Paper?
Another form of the straight line which we come across is general form:
Ax + By + C = 0
It can be useful for drawing lines by finding the y-intercept (put `x = 0`) and the x-intercept (put `y = 0`).
We also use General Form when finding Perpendicular Distance from a Point to a Line.
Draw the line 2x + 3y + 12 = 0.
1. What is the equation of the line perpendicular to the line joining (4, 2) and (3, -5) and passing through (4, 2)?
[Need a reminder? See the section on Slopes of Perpendicular Lines.]
2. If `4x − ky = 6` and `6x + 3y + 2 = 0` are perpendicular, what is the value of `k`?
Conic section: Straight line
Each of the lines and curves in this chapter are conic sections, which means the curves are formed when we slice a cone at a certain angle.
How can we obtain a straight line from slicing a cone?
We start with a double cone (2 right circular cones placed apex to apex):
If we slice the double cone by a plane just touching one edge of the double cone, the intersection is a straight line, as shown.
Didn't find what you are looking for on this page? Try search:
Online Algebra Solver
This algebra solver can solve a wide range of math problems. (Please be patient while it loads.)
Go to: Online algebra solver
Ready for a break?
Play a math game.
(Well, not really a math game, but each game was made using math...)
The IntMath Newsletter
Sign up for the free IntMath Newsletter. Get math study tips, information, news and updates each fortnight. Join thousands of satisfied students, teachers and parents!
Math Lessons on DVD
Easy to understand math lessons on DVD. See samples before you commit.
More info: Math videos