Writing an Equation From a Graph
Write linear equations from a graph by identifying the slope and y-intercept or using two points. Develop Grade 9 skills for interpreting and modeling graphs.
Key Concepts
Property First, identify the $y$ intercept ($b$) where the line crosses the $y$ axis. Next, calculate the slope ($m$) by finding the rise and run between two points. Finally, write the equation $y = mx + b$.
Examples A line crosses the y axis at $ 1$ and goes up 1 unit for every 2 units right. The equation is $y = \frac{1}{2}x 1$. A line has a y intercept of $2$ and goes down 3 units for every 1 unit right. The equation is $y = 3x + 2$.
Explanation Time to be a line detective! Find where the line hits the vertical y axis—that's your 'b'. Then, count the squares up/down and right between any two points to find your slope 'm'. Put them together to reveal the line's secret identity!
Common Questions
What key features help you graph writing an equation from a graph?
Identify intercepts, slope or vertex, and key points. Plot them systematically and connect to show the complete shape of the graph.
How do you find x-intercepts when graphing?
Set y = 0 and solve for x. These crossing points are critical for understanding the function's behavior and finding solutions.
What does the graph reveal about this topic?
Graphs show solutions visually as intercepts or intersection points, reveal the number of solutions, and display trends equations alone do not show.