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Find the equation of the line specified.
The line passes through the points (5,2) and (6,4)

a. y = 2x- 8

b. y = 4x - 8

c. y = 2x + 12

d. y= 2x + 2​

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Answer:

a. y = 2x - 8

General Formulas and Concepts:
Algebra I

Coordinate Plane

  • Coordinates (x, y)

Slope Formula:
[tex]\displaystyle m = \frac{y_2 - y_1}{x_2 - x_1}[/tex]

Slope-Intercept Form: y = mx + b

  • m - slope
  • b - y-intercept

Step-by-step explanation:

Step 1: Define

Identify given.

Point (5, 2)

Point (6, 4)

Step 2: Find Equation

Finding slope m:

Simply plug in the 2 coordinates into the slope formula to find slope m.

  1. [Slope Formula] Substitute in points:
    [tex]\displaystyle m = \frac{4 - 2}{6 - 5}[/tex]
  2. Evaluate:
    [tex]\displaystyle m = 2[/tex]
  3. [Slope-Intecept Form] Substitute in m:
    [tex]\displaystyle y = 2x + b[/tex]

∴ our slope m is equal to 2 and our preliminary equation is y = 2x + b.

Finding y-intercept b:

  1. [Preliminary Equation] Substitute in point:
    [tex]\displaystyle 2 = 2(5) + b[/tex]
  2. Simplify:
    [tex]\displaystyle 2 = 10 + b[/tex]
  3. Solve:
    [tex]\displaystyle b = -8[/tex]

∴ the y-intercept b is equal to -8.

Finding line equation:

  1. [Slope-Intercept Form/Preliminary Equation] Substitute in b:
    [tex]\displaystyle y = 2x - 8[/tex]

∴ the equation of the line is equal to y = 2x - 8.

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Topic: Algebra I

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