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9th grade · Math · Unit 4 of 22

Linear Relations

Slope, intercepts and graphs

What your child practices

Finding slope from points and graphs, reading y = mx + b, finding intercepts, deciding whether a point is on a line, spotting parallel lines, and using rates of change in stories.

New York State Learning Standards learning standard: AI-F.IF.6; AI-F.IF.7; AI-F.LE.2 · rate of change and key features of linear functions

How we explain it

Children can open this short lesson before they practice.

  1. A line has the equation y = mx + b.
  2. The slope m is rise ÷ run. The y-intercept b is where the line crosses the y-axis.
  3. Find the slope from two points on the line.

Example: A line goes through (0, 1) and (2, 5). What is its slope? Rise: 5 − 1 = 4. Run: 2 − 0 = 2. Slope: 4 ÷ 2 = 2. Answer: 2 (so y = 2x + 1)

Linear Relations in New York

In the New York State Learning Standards, this is unit 4 of 22 in 9th grade Math, after Multi-Step Equations and before Statistics in Society.

Gradelings describes a child's practice on this unit as Beginning, Approaching, Meeting or Exceeding (Four practice steps). That reflects practice, not a report-card mark: the teacher decides the mark.

Source: New York State Education Department (NYSED)

Sample questions

A taste of this unit. In the app, questions change every time and get easier or harder to match your child.

  1. Question 1

    What is the slope of the line through (1, 4) and (3, -2)?

    -5-5-4-4-3-3-2-2-1-1001122334455AB

    answer box

  2. Question 2

    Find the slope of the line through (0, -2) and (4, -3).

    -5-5-4-4-3-3-2-2-1-1001122334455AB
    • 1/4
    • -4
    • -1/4
    • 4

  3. Question 3

    What is the y-intercept of y = x + 6?

    answer box

  4. Question 4

    Which equation has slope 5 and a y-intercept of −1?

    • y = -5x − 1
    • y = 5x − 1
    • y = -x + 5
    • y = 5x + 1

  5. Question 5

    Is the point (6, 15) on the line y = 2x + 5?

    • No
    • Yes

  6. Question 6

    What is the x-intercept of y = 2x − 8?

    answer box

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