Key Concepts in Algebra 1

What is the y-intercept?

What is the x-intercept?

What is slope intercept form?

What is the slope of the line represented by y = x + 9?

Write the equation of the line whose slope is 5 and y-intercept is (0,-7).

What is the slope of the line represented by y = 5x - 7?

Write the equation of the line that passes through (0,-6) and (4,10).

Write the point-slope equation of the line that passes through (7, 3) whose slope is 2.

What is the x-intercept of the line 5x - 2y = 10?

Key Concepts in Algebra 1

Y-Intercept
- Defined as the point where the graph intersects the y-axis, represented as (0, y).
X-Intercept
- Defined as the point where the graph intersects the x-axis, represented as (x, 0).
Slope-Intercept Form
- The general equation for linear functions, expressed as ( y = mx + b ) where:
  - ( m ) is the slope
  - ( b ) is the y-intercept

Slope of Lines

For the equation ( y = x + 9 ):
- The slope is represented as ( 1 ) (or ( 1x )).
For the equation ( y = 5x - 7 ):
- The slope is ( 5 ).

Writing Equations of Lines

When given a slope of ( 5 ) and a y-intercept of (0, -7):
- The equation is formulated as ( y = 5x - 7 ).
For a line passing through the points (0, -6) and (4, 10):
- The equation determined is ( y = 4x - 6 ).

Point-Slope Form

To write the equation of a line using point-slope form passing through (7, 3) with a slope of ( 2 ):
- The equation is ( y - 3 = 2(x - 7) ).

Intercepts of a Line

For the line represented by ( 5x - 2y = 10 ):
- The x-intercept is (2, 0), and the y-intercept is (0, -5).

This quiz covers fundamental concepts in Algebra 1, including Y-Intercept, X-Intercept, and the Slope-Intercept Form. Additionally, it explores how to determine slopes from equations and write equations for lines based on given points and slopes. Test your understanding of these key algebraic principles.