# Every line drawn on a coordinate plane has a corresponding linear ```CP Geometry
Project #1: Writing Equations of lines
Name __________________________
Every line drawn on a coordinate plane has a corresponding linear equation.
Each linear equation is the locus of all points on the coordinate plane that make that equation true.
Linear equations are usually written using one of three forms:
1. Standard form:
𝐴𝑥 + 𝐵𝑦 + 𝐶 = 0
(A, B, and C are integer coefficients)
or 𝐴𝑥 + 𝐵𝑦 = 𝐶
2. Slope-intercept form:
𝑦 = 𝑚𝑥 + 𝑏
(m represents the slope of the line, and b represents the y-intercept)
3. Point-slope form:
𝑦 – 𝑦1 = 𝑚(𝑥 – 𝑥1 )
(m represents the slope of the line, and (𝑥1 , 𝑦1 ) is any point on the line.
Method I. Graphing a line using the Standard Form:
Put the equation into standard form (𝐴𝑥 + 𝐵𝑦 = 𝐶)
𝐶
1. Let 𝑥 = 0; solve for 𝑦 { 𝑦 = 𝐵 } which will result in the point ( 0,
This is the y-intercept (the point where the line crosses the y-axis.)
𝐶
Graph the point ( 0, ).
𝐶
𝐵
).
𝐵
𝐶
𝐶
2. Let 𝑦 = 0; solve for 𝑥 { 𝑥 = 𝐴 } which will result in the point (𝐴 , 0 ).
This is the x-intercept (the point where the line crosses the x-axis.)
𝐶
Graph the point (𝐴 , 0 ).
3. Draw the line connecting the two intercepts.
For example, to graph the line 2𝑥 + 3𝑦 = 12
3(0) + 2𝑦 = 12
2𝑦 = 12
1. Let 𝑥 = 0; Then
. Plot the point (0, 6)
𝑦=6
3𝑥 + 2(0) = 12
2. Let 𝑦 = 0; Then
3𝑥 = 12
𝑥=4
3. Connect the two points with a line.
. Plot the point (4, 0).
CP Geometry
Project #1: Writing Equations of lines
Name __________________________
Method II. Graphing an equation using slope-intercept form
Put the equation into slope-intercept form: 𝑦 = 𝑚𝑥 + 𝑏
1. Plot the y-intercept (0, 𝑏).
2. Calculate one other point using the slope.
Remember the slope is in the form 𝑚 =
∆𝑦
∆𝑥
=
𝑐ℎ𝑎𝑛𝑔𝑒 𝑖𝑛 𝑦
𝑐ℎ𝑎𝑛𝑔𝑒 𝑖𝑛 𝑥
=
𝑦2 − 𝑦1
𝑥2 − 𝑥1
Calculate the new 𝑥1 value as 0 + ∆𝑥.
Calculate the new 𝑦1 value as 𝑏 + ∆𝑦.
3. Plot the new point and draw the line connecting the two points.
For example, graph the line y 
2
2
x  1 or y  x  (1)
3
3
1. Plot the y-intercept (0, -1).
2. Calculate another point using the slope:
x1  0  3  3
y1  1  2  1
3. Graph the point (3, 1) and draw the line connecting the two points.
Graph each of the following equations. For the odd numbered equations use Method I, and for the
even numbered equations use Method II. Show all your work.
1). 2y = 3x − 8
4).
3
5
2
x −3y = 5
10). 3x = 6y + 8
2).
3
5
2
x −3y = 5
3). 3y − 7 = 4
5). 3x − 4y = 24
11).
2
3
1
6). 2x + 7y = 9
3
y−x+2 =5
12).
9−3x
2
6
= 5y
```