"Linear" equations are equations with just a plain old variable like "x", rather than something more complicated like x2 or x/y or square roots or such. Linear equations are the simplest equations that you'll deal with.
When plotted on a coordinate system, they will always form a line.
Forms of linear equations - Linear equations can be written in following forms
When plotted on a coordinate system, they will always form a line.
Forms of linear equations - Linear equations can be written in following forms
A linear equation can be written in multiple ways or forms.
An equation written in standard form can be transformed into slope intercept form or point slope form. The same way, an equation written in point slope form can be transformed into standard form.
An equation written in standard form can be transformed into slope intercept form or point slope form. The same way, an equation written in point slope form can be transformed into standard form.
Slope of a Linear equation
The measure of steepness of a line is called it's slope.
x-intercept and y-intercept
The graphical concept of x- and y-intercepts is pretty simple. The x-intercepts are where the graph crosses the x-axis, and the y-intercepts are where the graph crosses the y-axis.
Algebraically,
Algebraically,
- an x-intercept is a point on the graph where y is zero, and
- a y-intercept is a point on the graph where x is zero.
Standard form to Point Slope form
coming soon.
Standard form to Slope Intercept form
coming soon
Slope Intercept form to Standard form
coming soon
Slope Intercept form to Point Slope form
coming soon
Point Slope form to Slope Intercept form
coming soon
Point Slope form to Slope Intercept form
coming soon
Finding the x and y intercepts:
When Equation is given in Standard form
Remember x-intercept is a point where the line meets x-axis, and has y coordinate value as 0.
Plug in y=0 in the equation and solve for x.
This will give you (x-value, 0) as the x-intercept.
Also, remember y-intercept is a point where the line meets y-axis, and has x coordinate value as 0.
Plug in x=0 in the equation and solve for y.
This will give you (0, y-value) as the y-intercept.
When Equation is given in Slope Intercept form
Remember in slope intercept form, y=mx+b, b is y-intercept
That is point (0,constant in equation) is the y-intercept
Plug in y=0 in the equation and solve for x.
This will give you (x-value, 0) as the x-intercept.
When Equation is given in Point Slope form
Remember x-intercept is a point where the line meets x-axis, and has y coordinate value as 0.
Plug in y=0 in the equation and solve for x.
This will give you (x-value, 0) as the x-intercept.
Also, remember y-intercept is a point where the line meets y-axis, and has x coordinate value as 0.
Plug in x=0 in the equation and solve for y.
This will give you (0, y-value) as the y-intercept.
When 2 point on the line are given
If you know 2 points on the line, you can find slope using the slope formula
After you know the slope, use either of the points, and slope value, and write the equations in point slope form.
Finding Slope:
When Equation is given in Standard form
Use the formula for Slope for equation in standard form
When Equation is given in Slope Intercept form
Remember in slope intercept form, y=mx+b, coefficient of x is the slope
Slope is coefficient of x.
When Equation is given in Point Slope form
Remember in Point Slope form, y-y1=m(x-x1), m is the slope
Slope is the value multiplying (x-x1).
When 2 point on the line are given
If you know 2 points on the line, you can find slope using the slope formula.
Remember in slope intercept form, y=mx+b, coefficient of x is the slope
Slope is coefficient of x.
When Equation is given in Point Slope form
Remember in Point Slope form, y-y1=m(x-x1), m is the slope
Slope is the value multiplying (x-x1).
When 2 point on the line are given
If you know 2 points on the line, you can find slope using the slope formula.