Algebra 1 Chapter 5 Test - Study Notes

Algebra 1 Chapter 5 Test - Study Notes

• Finding the slope of a line:

  • Slope is calculated using the formula: (y₂ - y₁) / (x₂ - x₁), where (x₁, y₁) and (x₂, y₂) are two points on the line.
  • Example: For points (-2, 5) and (3, -4), the slope is (-4 - 5) / (3 - (-2)) = -9 / 5.

• Identifying slope and y-intercept from equations:

  • Equations in the form y = mx + b represent linear relationships, where 'm' is the slope and 'b' is the y-intercept. 
  • Example: For y = (-5/3)x + 2, the slope is -5/3 and the y-intercept is 2.

• Finding x and y intercepts:

  • The x-intercept is the point where a graph crosses the x-axis (y = 0).
  • The y-intercept is the point where a graph crosses the y-axis (x = 0).
  • Example: For the equation 4x - 5y = 20
    • x-intercept: set y = 0, 4x = 20, x = 5
    • y-intercept: set x = 0, -5y = 20, y = -4

• Writing equations of lines:

  • Point-slope form: y - y₁ = m(x - x₁), where 'm' is the slope and (x₁, y₁) is a point on the line.
  • Slope-intercept form: y = mx + b, where 'm' is the slope and 'b' is the y-intercept.
  • Standard form: Ax + By = C, where A, B, and C are integers.

• Parallel and Perpendicular Lines:

  • Parallel lines have the same slope.
  • Perpendicular lines have slopes that are negative reciprocals of each other.

• Real-world situations and correlation:

  • A strong negative correlation indicates that as one variable increases, the other variable tends to decrease.

• Coordinate Plane Problems:

  • Problems involving finding the equation of a line parallel to a given side of a triangle in the coordinate plane. 
  • Students need to find the slope of the given side, set up the equation using the point-slope form and the given points, and then convert to slope-intercept form.