1. Unit 5 Writing the Equation of a Line
HSA ALGEBRA
Unit 5
Writing the Equation of a Line

2. You can also find the slope (m) of the line
The Equation of a Line
Given any two points in the coordinate plane, you can draw a line through them. x y l
(X2,Y2)
(X1,Y1)
rise
You can also find the slope (m) of the line
run
m = Y2 – Y1
X2 – X1
m = rise
run

3. The Equation of a Line y (X2,Y2) x (X1,Y1)
A line contains infinite points. x y
The Equation of the Line is the relationship between the coordinates of the infinite points on the line.
It has three different forms:
Slope-Intercept
Point-Slope
Standard
(X2,Y2)
(X1,Y1)

4. The Equation of a Line has three Different Forms
Slope-Intercept Y = mX + b
where m is the slope and b is the y-intercept
Point-Slope Y – Y1 = m (X – X1)
where m is the slope and X1 and Y1 are the coordinates of one of the given points
Standard AX + BY = C
where A, B, and C are integers, and A is positive

5. The Equation of a Line has three Different Forms
We will focus on two Forms:
Slope-Intercept Form Y = mX + b, where m is the slope and b is the y-intercept
Point-Slope Form Y – Y1 = m (X – X1), where m is the slope and X1 and Y1 are the coordinates of one of the given points

6. How can you find the Equation of a line?x y l
You need two points.
They can be the intercepts,
y-intercept
(0,Y)
(X2,Y2)
(X1,Y1)
They can be any two points, or…
…the combination of an intercept and a point.
x-intercept
(X,0)

7. Finding the Equation of a Line given two pointsx y l
First step - find the slope (m) of the line
(4,6)
m = rise
run
rise
m = Y2 – Y1
X2 – X1
(-3,-2)
m = 6 – (-2)
4 – (-3)
run
m = 8 7

8. Finding the Equation of a Line given two pointsx y l
Second step - substitute the slope (m) of the line and the coordinates of either point in the Point-Slope Form of the Equation
(4,6)
(-3,-2)
rise
Y – Y1 = m(X – X1)
Y – 6 = 8 (X – 4)
run
m = 8 7

9. Finding the Equation of a Line given two points
Third step - solve the equation using cross-multiplication, distributive property and opposite operations to isolate the variables to the left and constant (numbers) to the right
Y – 6 = 8(X – 4) 7
cross-multiplication
7(Y – 6) = 8(X – 4)
distributive property
7Y – 42 = 8X – 32
opposite operations
– 8X + 7Y =

10. Finding the Equation of a Line – Practice 1
Write the equation of the line through points (9, 5) and (-3, -1).
First step - find the slope (m) of the line
m = Y2 – Y1
X2 – X1
m = – 1 – (5)
– 3 – 9
m = – 6
– 12
m = 1 2
Second step - substitute the slope (m) and the coordinates of either point into the Point-Slope Form
Y – Y1 = m(X – X1)
Y – (– 1) = 1(X – (-3))

11. Finding the Equation of a Line – Practice 1
Third step - solve the equation using cross-multiplication, distributive property, and opposite operations to isolate the variables and constant.
Y – (-1) = 1(X – (-3))
Multiply both sides by two
2(Y + 1) = 1(X + 3)
distributive property
2Y + 2 = X + 3
opposite operations
2Y = X
2Y = X + 1
Solve for Y
Y = ½ X – ½

12. Finding the Equation of a Line – Practice 2
Write the equation of the line with slope –3/4 going through point (-2, 5).
First step - find the slope (m) - given
m = -3 4
Second step - substitute the slope (m) of the line and the coordinates of the point in the Point-Slope Form
Y – Y1 = m(X – X1)
Y – 5 = - 3 (X – (-2))

13. Finding the Equation of a Line – Practice 2
Third step - solve the equation using cross-multiplication, distributive property and opposite operations
Y – 5 = - 3(X – (-2)) 4
cross-multiplication
4(Y – 5) = – 3(X + 2)
distributive property
4Y – 20 = – 3X - 6
opposite operations
4Y = – 3X
4Y = – 3X + 14
Y = – ¾ X + 7/2

14. Finding the Equation of a Line – Practice 3
What is the equation for the line below? x y
First step - Find the slope (m) In this case, identify two points on the line.
(- 3, 3)
y-intercept = -2
m = - 2 – 3
0 – (- 3)
m = 3

15. Finding the Equation of a Line – Practice 3
Second step - substitute the slope (m) of the line and the coordinates of one of the points in the Point-Slope Form of the Equation
m = - 5 3
(3, - 3) or (0, - 2)
Y – Y1 = m (X – X1)
Y – (- 2 ) = - 5 (X – 0)

16. Finding the Equation of a Line – Practice 3
Third step - solve the equation using cross-multiplication, distributive property and opposite operations
Y – (- 2) = - 5 (X – 0)
cross-multiplication
3(Y + 2) = – 5(X)
distributive property
3Y + 6 = – 5X
opposite operations
3Y = – 5X – 6
Y = – 5/3 X – 2

17. Find the Equation of a Line – Practice 4x y
What is the Standard form of the equation for line s?
5x + 2y = 20
What is the slope-intercept form of the equation for line s?
y = - 5x

18. Find the Equation of a Line – Practice 4x y
What is the slope for line s?
m = - 5/2
What is the x-intercept for line s?
x-intercept is 2 (2,0)

19. Questions ?
Good luck!