WME@Kimpton Middle
## Straight Lines and Their EquationsThe - A straight line is
*straight*because any two segments on the line form an 180-degree angle with each other. - The shortest path between any two points on a straight line is through the points connecting them on the line.
- The
*slope*of a straight line measures how slanted the line is. -
The
*y-intercept*is the`y` coordinate of the point where the line intercepts the y-axis and the*x-intercept*is the`x` coordinate of the point where the line intercepts the x-axis.The y-intercept of the line in this graph is exactly . The x-intercept of the line in this graph is almost . - A straight line in the xy-plane always has an equation in this general
form
`a x + b y + c = 0` where `a` is the*coefficient*of`x` ,`b` is the*coefficient*of`y` , and`c` is the*constant term*.A straight line always has an equation in this form and the graph of any equation in this form is a straight line. Any point with coordinates `(x` is on the line if it_{1}, y_{1})*satisfies the equation*which means if you subsitute the value`x` for_{1}`x` and the value`y` for_{1}`y` in the euqation, the result`a x` is actually equal to zero._{1}+ b y_{1}+ c
Assuming the x-axis represents the horizontal and the y-axis reprents the vertical, then the slope of a straight line measures
how slanted or steep the line is relative to the horizontal or vertical.
Specifically,
Written out explicitly, this means
computed using any two points Given the equation of a line, we can find its slope using the above
definition. But there is another way that may be easier.
By putting the equation of a line in the
you can easily obtain the value for Let's try taking an equation and transform it into the slope-intercept form. First, enter a line equation of your choosing: x + y + = 0 And it is displayed here. Numbers are rounded to the nearest hundredth. You can transform this equation into the slope-intercept form by *solving for*through a sequence of steps, by adding, subtracting, multiplying or dividing both sides with the same quantity.`y` in terms of`x` -
Enter a number or a multiple of `x`(for example`2 x`and`-4 x`) and click a button and the operation will be applied to**both sides**of the latest equation and produce an equvalent new equation:`x` Try and do another equation.
Here is a diagram where you can interactively enter a straight line. Then you can move the y-intercept or rotate the line by dragging the intercept point or the line. As the line changes, you'll also see the equation for the line change. |
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