Algebra 1 Unit 4 study games — Writing Linear Equations.
This unit covers point-slope form, standard form, writing from graphs and linear modeling — essential concepts for Algebra 1. Use our interactive study games to test your understanding, or review questions in traditional format below.
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This unit covers point-slope form, standard form, writing from graphs and linear modeling — essential concepts for Algebra 1. Use our interactive study games to test your understanding, or review questions in traditional format below.
Key Concepts Breakdown
1 Point-Slope Form
Point-slope form is y - y₁ = m(x - x₁), where m is the slope and (x₁, y₁) is a known point on the line. Students must be able to write the equation given a point and a slope, or given two points. They also need to convert point-slope form to slope-intercept form.
Key Points
- Formula: y - y₁ = m(x - x₁); plug in slope and one point directly
- Given two points, calculate slope first: m = (y₂ - y₁)/(x₂ - x₁), then use either point
- To convert to slope-intercept form, distribute m and solve for y
- The equation is not unique when two points are given — either point produces an equivalent equation
Write the equation of the line through (2, -3) with slope 4.
Substitute m = 4, x₁ = 2, and y₁ = -3 into y - y₁ = m(x - x₁) to get y - (-3) = 4(x - 2), which simplifies to y + 3 = 4(x - 2). To convert to slope-intercept form, distribute: y + 3 = 4x - 8, then subtract 3 from both sides to get y = 4x - 11.
2 Standard Form
Standard form is Ax + By = C, where A, B, and C are integers, A is non-negative, and A and B are not both zero. Students must convert between standard form and slope-intercept form, and identify the slope and intercepts from standard form. Exams often ask students to rewrite equations or identify which form a given equation is in.
Key Points
- Standard form: Ax + By = C with A, B, C as integers and A ≥ 0
- x-intercept: set y = 0 and solve for x; y-intercept: set x = 0 and solve for y
- To find slope from standard form, solve for y: slope = -A/B
- To convert from slope-intercept to standard form, move the x-term to the left side and clear any fractions by multiplying through
Convert y = (2/3)x - 4 to standard form.
Multiply every term by 3 to eliminate the fraction: 3y = 2x - 12. Move the x-term to the left by subtracting 2x from both sides: -2x + 3y = -12. Since A must be non-negative, multiply the entire equation by -1 to get 2x - 3y = 12.
3 Writing Equations From Graphs
Students must be able to read a graph and write the equation of the line in slope-intercept form. This requires identifying the y-intercept directly from the graph and calculating the slope by choosing two clear lattice points. This skill is almost always tested on exams in both multiple-choice and free-response formats.
Key Points
- Identify the y-intercept: the point where the line crosses the y-axis — this is b in y = mx + b
- Choose two points with integer coordinates clearly on the line to calculate slope: m = rise/run
- Rise is the vertical change (positive up, negative down); run is the horizontal change (positive right)
- A horizontal line has slope 0 (y = b); a vertical line has undefined slope (x = a)
A line passes through (0, 5) and (3, -1). Write its equation in slope-intercept form.
The y-intercept is 5 because the line crosses the y-axis at (0, 5), so b = 5. The slope is m = (-1 - 5)/(3 - 0) = -6/3 = -2. Substituting into y = mx + b gives the equation y = -2x + 5.
4 Linear Modeling
Linear modeling means writing a linear equation to represent a real-world situation and using it to make predictions. Students must identify the slope as the rate of change and the y-intercept as the starting value from context. Exams frequently ask students to interpret what the slope and y-intercept mean in the situation, not just calculate them.
Key Points
- Slope = rate of change (e.g., cost per item, miles per hour, dollars per month)
- Y-intercept = initial value or starting amount when x = 0 (e.g., flat fee, starting balance)
- Write the equation from a table by finding the constant rate of change between rows
- Use the equation to predict values by substituting a given x (or y) and solving
A phone plan charges a $20 flat monthly fee plus $0.10 per text message. Write an equation for the total monthly cost C based on the number of texts t, then find the cost for 150 texts.
The flat fee is the y-intercept (starting value), so b = 20, and the cost per text is the slope, so m = 0.10. The equation is C = 0.10t + 20. Substituting t = 150 gives C = 0.10(150) + 20 = 15 + 20 = $35.
Questions, answered.
What is Writing Linear Equations?
Writing Linear Equations is Unit 4 of Algebra 1, covering point-slope form, standard form, writing from graphs and linear modeling.
How to study for Algebra 1 Unit 4?
Start with the Quick Summary above, review the Key Concepts, then test yourself with our interactive study games. Aim for 80%+ accuracy before moving on.
How many questions are in this unit?
This unit has 27+ review questions across 5 different game modes.