Writing an Equation from a Graph
Writing a linear equation from a graph is a foundational Grade 11 Algebra 1 skill from enVision Chapter 2 that requires identifying the y-intercept and calculating slope from the graph. The process: locate where the line crosses the y-axis for the y-intercept b, then pick two clear points to find slope m = rise/run, and substitute into y = mx + b. For a line crossing at (0, 3) and passing through (2, 7), the slope is (7-3)/(2-0) = 2, giving y = 2x + 3. For a line through (0, -1) and (4, 1), slope is 1/2, giving y = ½x - 1.
Key Concepts
To write an equation from a graph in slope intercept form $y = mx + b$: 1. Identify the y intercept $b$ where the line crosses the y axis 2. Find the slope $m = \frac{\text{rise}}{\text{run}}$ using two clear points on the line 3. Substitute $m$ and $b$ into $y = mx + b$.
Common Questions
How do you write an equation from a graph?
Identify the y-intercept where the line crosses the y-axis, then calculate slope using two points with m = rise/run. Substitute both values into y = mx + b.
What is the equation of a line crossing (0, 3) and passing through (2, 7)?
Slope = (7-3)/(2-0) = 2, y-intercept = 3. The equation is y = 2x + 3.
What is the equation for a line through (0, -1) and (4, 1)?
Slope = (1-(-1))/(4-0) = 2/4 = 1/2. Equation: y = (1/2)x - 1.
What is the y-intercept and how do you read it from a graph?
The y-intercept is the point where the line crosses the y-axis. Its coordinates are (0, b), so you read the b value directly from the graph.
What does rise/run mean for slope?
Rise is the vertical change (up or down) between two points; run is the horizontal change (left or right). Slope = rise ÷ run.
Why should you use two clearly readable points when finding slope from a graph?
Points that fall exactly on grid intersections give precise integer or simple fraction values for rise and run, minimizing estimation errors.