Write Linear Equations from Two Points

TEKS A.2B

Write Linear Equations Given 2 Points & Slope

When given a slope and a point or 2 points and a slope, we can write the equation of a line in Slope-Intercept form, Point-Slope form, and Standard form.

There are several ways we can do this!

We could use the Point-Slope Method:

Or we could use the Slope-Intercept Method:

My Favorite is the Calculator Method!

​When given 2 points, you can find the slope, m, and the y-intercept, b, using the calculator!

1.) Go to the Home Screen and create a New Document. Answer No to the save question.
2.) Press 4 for Add Lists & Spreadsheets.
3.) Scroll up to the A column and type x; Then type y in the B column.
4.) Type your 2 points in the table.
5.) Press Menu/4-Statistics/1-Stat Calculations/3-Linear Regression, mx+b
6.) Double click under the X-list to select x; then click on the Y-list to select y.
7.) Press Enter. The calculator will tell you the m (slope) and b (y-intercept).
8.) Try it: Use the points (1, 2) and (5, 10). Did you get m = 2 and b = 0?

Multiple Choice

Which of these is the slope formula?

• $$m=\frac{x_2-x_1}{y_2-y_1}$$  

• $$m=\frac{y_2-y_1}{x_2-x_1}$$  

• $$m=\frac{x_2+x_1}{2},\frac{y_2+y_1}{2}$$  

• $$m=\sqrt[]{\left(x_2-x_1\right)^2+\left(y_2-y_1\right)^2}$$  

Multiple Choice

What does the "m" represent in $$y=mx+b$$  

• y-intercept

• measurement

• slope

• nothing

Multiple Choice

What does the "b" represent in $$y=mx+b$$  

• y-intercept

• nothing

• slope

• base

Multiple Choice

Find the slope of the line going through points

(2, -5) and (0, 1). Use the Slope Formula.

• -2

• -3

• 2

• 3

Slope-Intercept: y = mx+b

• Used for graphing linear equations

• Need a slope (m) and y-intercept (b)

Multiple Choice

Which of these represents slope-intercept form of a linear equation?

• y - y₁ = m(x-x₁)

• Ax + By = C

• y = mx + b

• y=kx

Multiple Choice

What is the slope in the equation y = 2x + 3?

• 2

• 3

• 5

• Cannot be Determined 

Multiple Choice

What is the y-intercept in the equation $$y=4x+3$$  

• 3

• 4

• 3x

• 4x

Multiple Choice

Write the equation of a line that contains the point (3, 5) and has a slope of 3 in slope-intercept form ( Plug in the point and slope into y = mx + b).

• y = 3x - 4

• y - 5 = 3(x-3)

• y = 3x + 14

• y + 5 = 3(x+3)

Multiple Choice

What is an equation in Slope-Intercept form for the line that passes through the coordinates (-1,2) and (7,6)? (Try the Linear Regression Method.)

• y = (1/2)x + 2.5

• y = (1/2)x - 5

• y = 3x + 4

• y = -3x + 4

Point-slope Form: y - y₁ = m(x - x₁)

• Useful when you are given a point (x₁, y₁) and slope (m)

• Plug in the opposite values of points into formula

Multiple Choice

Which of these represents point-slope form of a linear equation?

• y - y₁ = m(x - x₁)

• Ax + By = C

• y = mx + b

• y=kx

Multiple Choice

For the equation
y + 1 = -3 (x - 5),
the line contains the point (5, -1) and has a slope of?

• -1

• 1

• -3

• 5

Multiple Choice

Write the equation in point-slope form of the line that passes through the given point and has the given slope.
(4, -7); m = -1/4

• y + 7 = -1/4(x - 4)

• y - 4 = -1/4(x + 7)

• y + 7 = 4(x - 4)

• y - 7 = -1/4(x - 4)

Multiple Choice

Write the equation in point-slope form for the line that contains the points
(-2, -3) and (4, 3)

$$m\ =\ \frac{y_2\ -y_1}{x_2\ -\ x_1}$$

• y - 3 = 1(x - 2)

• y + 3 = 1(x + 2)

• y -3 = -1(x + 2)

• y + 3 = -1(x - 2)

Standard Form : Ax + By = C

• Form is useful to convert to a different form.

• A, B, and C are all whole numbers.

Multiple Choice

Which of these represents standard form of a linear equation?

• y - y₁ = m(x-x₁)

• Ax + By = C

• y = mx + b

• y=kx

Multiple Choice

Which equation is written in STANDARD form?

• y = 1/2x + 2

• y - 3 = -5(x + 2)

• -7x + 2y = 9

• 3x + 2 = y

Multiple Choice

Convert from standard form to slope intercept form: 3x - 2y = -16 (1. Move the x-term to the right side; 2. Divide all terms by the coefficient.)

• y = -3x - 8

• y = -3x + 8

• y = -3/2x - 8

• y = 3/2 x + 8

Multiple Choice

What is the slope of the line 5x - 10y = 21?

(Convert to Slope-Intercept form first.)

• -5/10

• -10/5

• 1/2

• -2

Multiple Choice

Convert from Slope-Intercept form to Standard form:

y = 1/4 x + 4 (First, undo the fraction by multiplying both sides by 4.)

• x + 4y = 8

• x - 4y = -16

• y = x + 16

• 4y + x = 8

Multiple Choice

Write the standard form equation that passes through (0, -1) and (-6, -9). (STEPS: 1. Find m and b; 2. Write in Slope Intercept form; 3.) Convert to Standard form)

• -3x + 4y = - 4

• -4x + 3y = -3

• y = 4/3x - 1

• 3x - 4y = 1

Poll

Are you Clear or Cloudy on this lesson?

• I am Clear. I could teach it to others.

• I am Cloudy. I should re-do this lesson.