Virginia SOL 8.PFA.3

8.PFA.3 is a Standards of Learning standard. These are the knowledge and skills expectations under it.

• 8.PFA.3.a

  Determine how adding a constant (b) to the equation of a proportional relationship y = mx will translate the line on a graph.

• 8.PFA.3.b

  Describe key characteristics of linear functions including slope (m), y-intercept (b), and independent and dependent variables.

• 8.PFA.3.c

  Graph a linear function given a table, equation, or a situation in context.

• 8.PFA.3.d

  Create a table of values for a linear function given a graph, equation in the form of y = mx + b, or context.

• 8.PFA.3.e

  Write an equation of a linear function in the form y = mx + b, given a graph, table, or a situation in context.

• 8.PFA.3.f

  Create a context for a linear function given a graph, table, or equation in the form y = mx + b.

01

What Students Need to Do

Students translate linear relationships among equations, tables, graphs, and real situations. They identify slope, y-intercept, and variables, explain vertical shifts, and use each form to solve problems.

02

What Mastery Looks Like

A student can move accurately among a graph, table, equation, and context. The student can identify and interpret the slope and y-intercept, label both variables, and explain how changing the constant shifts the graph.

03

Common Misconceptions

Students may confuse slope with the y-intercept or calculate slope using inconsistent point order. They may think adding a constant changes the slope or moves the line sideways. They may also reverse the independent and dependent variables.

04

How to Assess It

Give students y = -2x + 3. Ask them to make a table for x = -1, 0, and 2, graph the line, label its slope and intercept, and write a matching context.

1. 01

   Graph y = 2x and y = 2x + 3 on transparent grids, overlay them, and mark how each point moves.

2. 02

   Ask, “How can two lines have the same rate but different starting values?” Students cite a graph, table, and context.

3. 03

   Give groups cards showing equations, tables, graphs, and situations; teams match four representations and justify the slope and intercept.

4. 04

   Model a taxi fare with a $4 starting fee and $2 per mile, then create its equation, table, graph, and fare questions.

• 6.PFA.3

  The student will write and solve one-step linear equations in one variable, including contextual problems that require the solution of a one-step linear equatio...

• 6.PFA.4

  The student will represent a contextual situation using a linear inequality in one variable with symbols and graphs on a number line. 

• 7.PFA.3

  The student will write and solve two-step linear equations in one variable, including problems in context, that require the solution of a two-step linear equati...

• 7.PFA.1

  The student will investigate and analyze proportional relationships between two quantities using verbal descriptions, tables, equations in y = mx form, and grap...