Algebra 1Chapter 5

Standard form, point slope form, and slope intercept

Perpendicular lines

Standard Form

Must write the equation in the form Ax+By=C

Find 2 points on the line whose coordinates are both integers

Use the values of the coordinates to fine the slope of the line using the formula m=y2-y1/x2-x1

Standard Form Cont….

Use values found for slope and a coordinates

Then write it in point-slope form y-y1=m(x-x1)

Solve for y

Standard Form Cont….

Example: M= 5, (6,3) Y-3=5(x-6) Write equation Y-3=5x-30 Distribute the 5 Y=5x-27 Add 3 to both

sides

Standard Form Cont….

Then to make it into standard form we may need to add or subtract from either side

Example: Y=5x-27 Add 27 to both sides Y+27=5x Subtract y from both

sides 27=5x-y This is in Standard Form

Recap

Point-slope formy-y1=m(x-x1)

Standard FormAx+By=C

Slope formulam=y2-y1/x2-x1

Slope Intercept Form

An equation of the line with slope m and y-intercept

To find y-intercept, find where the point crosses the y-axis or where x=0

It’s the y-intercept of that point Ex: (0,5) so the intercept is 5

Slope Intercept Form Cont….

Then use slope formula m=y2-y1/x2-x1

Use the point that you found for the y-intercept

Then find another point whose coordinates are integers

Slope Intercept form Cont….

Once you have found the y-intercept

Also once found the slope Plug each one into the formula

y=mx+b in the correct places

Slope Intercept Form Cont….

Example:Given points (0,6) (3,12)

Find the slope and the y-interceptM=12-6/3-0=6/3=2Plug into y=mx+b

Slope Intercept Form Cont….

Use the point that crosses the y-axis

M=2, y-intercept=6y=2x+6

Remark: positive slope rises left to right, negative slope falls left to right

Perpendicular Lines

To find a line perpendicular to another

First we need to know the slope of the first line

Perpendicular lines have the opposite reciprocal of the normal line

Perpendicular Lines Cont…

Once found the slope of the perpendicular line

Use the point slope equation to find the equation of that line

Then solve for y and put in slope intercept form

Perpendicular Lines Cont….

Example:Given two points (5,10)

(8,16) Find the equation of the normal

and perpendicular First: Find the slope of the

normal line

Perpendicular Lines Cont….

M=16-10/8-5=6/3=2 Plug into point slope to find

equation of the normal line, pick either point

M=2 (5,10)y-10=2(x-5)y-10=2x-10y=2x

Example Cont….

Now find the perpendicular line The slope is opposite and the

reciprocal of the normal M=-1/2, then just pick a point

again and plug it into point slope formula

Example Cont….

M=-1/2, (5,10) Y-10=-1/2(x-5) Y-10=-1/2x+5/2 Y=-1/2x+25/2 Now we have both equations