teach me graphing of simple line equations with x and y variables, and matching those to graphs

视频信息

答案文本 复制

视频字幕 复制

Welcome to graphing linear equations. A linear equation in two variables can be written in the form y equals m x plus b, where m is the slope of the line and b is the y-intercept. The y-intercept is the point where the line crosses the y-axis. For example, in the equation y equals 2x plus 1, the slope is 2 and the y-intercept is at the point (0,1). One method for graphing a linear equation is by plotting points. First, choose some x-values. Then, calculate the corresponding y-values by substituting each x-value into the equation. Next, plot these ordered pairs on the coordinate plane. Finally, draw a straight line through these points. For our example y equals 2x plus 1, if we choose x equals negative 1, 0, and 1, we get the points negative 1 comma negative 1, 0 comma 1, and 1 comma 3. When we plot these points and draw a line through them, we get the graph of y equals 2x plus 1. Another method for graphing a linear equation is using the slope and y-intercept. First, identify the y-intercept, which is the point where the line crosses the y-axis. For y equals 2x plus 1, the y-intercept is at the point (0, 1). Next, use the slope to find another point on the line. The slope m equals 2, which we can write as 2 over 1. This means that for every 1 unit we move to the right, we move up 2 units. Starting from the y-intercept at (0, 1), if we move right 1 unit and up 2 units, we reach the point (1, 3). Finally, draw a straight line through these two points to graph the equation y equals 2x plus 1. Now, let's learn how to match a graph to its equation. First, find the y-intercept, which is the point where the line crosses the y-axis. In our example, the y-intercept is at (0, -1). Next, identify another point on the line. Let's use the point (2, 1). Then, calculate the slope using the formula: m equals y2 minus y1 divided by x2 minus x1. Substituting our points, we get m equals 1 minus negative 1, divided by 2 minus 0, which equals 2 divided by 2, or 1. Finally, write the equation in slope-intercept form: y equals mx plus b. With m equals 1 and b equals negative 1, our equation is y equals x minus 1. This is the equation of the line shown on the graph. Let's summarize what we've learned about graphing linear equations. Linear equations can be written in the form y equals mx plus b, where m represents the slope and b represents the y-intercept. To graph a line, you can either plot points by choosing x-values and calculating corresponding y-values, or use the slope-intercept method by plotting the y-intercept and using the slope to find additional points. The slope represents the rate of change, calculated as rise over run or the change in y divided by the change in x. The y-intercept is the point where the line crosses the y-axis, at the coordinate (0,b). To find an equation from a graph, identify the y-intercept and calculate the slope using two points on the line, then substitute these values into the slope-intercept form. These skills are fundamental for understanding linear relationships in algebra, geometry, and real-world applications.