LINEAR EQUATIONS AND GRAPHS Unit Overview This unit is about linear equations and their graphs. In this unit, you will learn how to write equations of lines using the slope‑intercept form of a line and the point‑slope form. You will investigate transformations of the parent function, y = x, and learn how to graph linear equations in standard form using the x- and y-intercepts. You will take a closer look at horizontal and vertical lines. The unit will conclude with a discussion of the equations and graphs of parallel lines and perpendicular lines. Slope-Intercept Form The Slope-Intercept Form of a Linear Equation (07:15) Converting Equations Into Slope-Intercept Form (05:44) Parent Functions and Transformations Use a graphing calculator or knowledge from above to answer the below questions. Also, there is a graphing program online at https://www.desmos.com/calculator. Describe the translation for y = 3x from the parent function y = x. The steepness of the line (slope) will change from m = 1 (1/1) to m = 3 (3/1). "Click here" to check the answer. How does the y-intercept change? The y-intercept remains 0. The graph passes through (0, 0). "Click here" to check the answer. View the graphs.
"Click here" to view both graphs. Describe the translation for y = x + 3 from the parent function y = x. The graph is translated 3 units up and passes through the y-axis at (0, 3). "Click here" to check the answer.
The slope (m = 1) remains the same (rise / run = 1 / 1). "Click here" to check the answer. How does the y-intercept change? The y-intercept changes from (0, 0) to (0, 3). "Click here" to check the answer. View the graphs.
The slope of the line is now negative and goes through Quadrants II and IV. "Click here" to check the answer.
The rise over run is down 1, then right one. "Click here" to check the answer. Describe a second way to count out the slope (rise / run) of the graph. The rise over run is up 1, then left 1. "Click here" to check the answer. How does the y-intercept change? The y-intercept remains 0. The graph passes through (0, 0). "Click here" to check the answer. View the graphs.
Describe the translation for y = 2x – 5 from the parent function y = x. The graph is translated 5 units down and the slope becomes steeper. "Click here" to check the answer. How does the slope change? The steepness of the line (slope) changes from m = 1 (1/1) to m = 2 (2/1). "Click here" to check the answer. How does the y-intercept change? The y-intercept changes from (0, 0) to (0, –5). "Click here" to check the answer. View the graphs.
Using Intercepts to Graph Equations in Standard Form (10:05)
What would the equation look like in standard form? –x + y = –1 "Click here" to check the answer.
x – y = 1 "Click here" to check the answer. Equations of Horizontal and Vertical Lines
Sample Answer: (0, –2), (–5, –2), (3, –2), (100, –2) "Click here" to check the answer.
Sample Answer: (3, 0), (3, –4), (3, 10), (3, –1000) "Click here" to check the answer. Negative, Positive, Zero, and Undefined Slopes (05:33) Parallel and Perpendicular Lines |