1. Write Equations of Lines

2. Slope Intercept Form: y = mx + b
-Find the equation of a line when you are given the slope of the line and any point on the line.
-Find the equation of a line when you are only given two points on the line

3. Steps to Write the Equation of a Line in Slope-Intercept Form
Use the equation y = mx + b
Plug the slope into the m spot if it’s given (or calculate the slope from 2 points then plug in)
Plug in the x and y values of one point (x,y) into the equation
Solve that equation for b
Plug the solution into the equation for the b value. Final equation will have x and y as variables and numbers as m and b

4. Write an equation of the line that passes through the point (6,-3) with a slope of -2.
Follow the steps:
y = mx + b
-3 = -2(6) + b (plug in given m, x, and y)
-3 = b (solve for b, add 12 to both sides)
9 = b
y=-2x+9
(plug in the m and b value into final equation)

5. Find the equation of a line with a slope of 4 and a point of (8, 3) on the line.
Follow the steps:
y = mx + b
3 = 4(8) + b (plug in m, x, and y)
3 = 32 + b (solve for b, subtract 32 from both sides)
-29 = b
y= 4x (plug in the m and b value)

6. Find an equation for a line that passes through these points (1,6) and (3,-4)
First find the slope of the line.
Let x1, y1 be (1,6) and x2, y2 be (3,-4).
M = y2 -y1 = -4 – 6 = = x2-y – -5

7. Now we know the m = -5 Pick either point
Now we know the m = -5 Pick either point. Let’s use (1,6) so x = 1, and y = 6.
Next solve for b.
Substitute into y= mx + b.
6= (-5)(1) + b
6= -5 +b
11=b The y- intercept is b=11.
So the final equation is: y = -5x + 11
Note - You can use either point in the equation and get the same answer.

8. Write an equation in slope-intercept form for the following points: (-3,2) and (5,-2).
The slope of the line is:
m = y2-y1 = = -4 = -1
x2-x (-3)
To find the y- intercept, substitute the slope for -½ and use (-3,2 ) for (x,y) in the slope-intercept form.
2= (-1/2)(-3) + b
2= 3/2 + b
½= b
Equation y= -½x + ½