slope intercept form
point slope form
where m is the slope and (x1, y1) is a point on the
line
This is another format for straight line equations. Use when you know a point and the slope; it helps find the y-intercept
y-y1=m(x-x1)
y - intercept
the y-coordinate of the point where the line crosses the y-axis
How to Write a Linear Function
Ex: Write an equation for the linear function � with the values �(0) = 5 and �(4) = 17.
1 - Write �(0) = 5 as (0, 5) and �(4) = 17 as (4, 17)
2 - Calculate the slope using the formula
3 - The y-intercept is 5 because the line crosses at (0,5)
Write in slope intercept form: y = mx + b
How to Write an Equation of a Line in Slope-Intercept Form
1 - Identify the slope m. You can use the slope formula if you know two points on the line.
2 - Find the y-intercept. Use the point-slope formula with the slope and one point
Standard Form
can be used to find the x- and y-intercepts.
Ax + By = C
A, B, C are integers (no fractions or decimals)
A should be positive
Slope Formula
What do you need to write the equation of a line?
the slope and the y-intercept
To write the equation of a line that passes through the point with the given slope
plug the slope and a point into y-y1=m(x-x1)
solve the equation
To write the equation of a line in slope intercept form that passes through two points
use the formula to find the slope
plug the slope and a point into y -y1=m(x-x1)
solve for y
Parallel Lines
If two nonvertical lines in the same plane have the same slope, then they are parallel.
If two nonvertical lines in the same plane are parallel, then they have the same slope.
To Write an Equation of a Parallel Line:
Write an equation of the line that passes through (-3, -5) and is parallel to the line y = 3x - 1
1 - Identify the slope (in this case = 3)
2 -plug the slope and point into y-y1=m(x-x1)
3. solve for y
Perpendicular Lines
If two nonvertical lines in the same plane have slopes that are negative reciprocals, then the lines are perpendicular.
If two nonvertical lines in the same plane are perpendicular, then their slopes are negative reciprocals.
To determine whether lines are parallel or perpendicular
write all equations in slope-intercept form ( y = mx + b)
compare their m value: if the same, then parallel; if negative reciprocals, then perpendicular
Slope and y intercept from a equation written in standard form
from an equation written in standard form
Ax+By=C
the slope is :m=-A/B
the y-intercept is: (0,C/B)
equation of a horizontal line that crosses (a,b)
y=b
equation of a vertical line that crosses (a,b)
x=a
slope of a horizontal line
m=0
slope of a vertical line
undefined
the slope of a line that raises from left to rigth
positive
the slope of a line that falls from left to rigth
negative