Math 8a Unit 7 Lesson 12: Graphing Linear Equations connections academy

Answer 1

In this lesson, you will learn about graphing linear equations. A linear equation is an equation that can be written in the form y = mx + b, where m and b are constants.

To graph a linear equation, you need to plot a few points and then connect them with a straight line. The equation y = mx + b represents a straight line with a slope of m and a y-intercept of b.

You can find the slope of a line by using the formula m = (y2 - y1) / (x2 - x1), where (x1, y1) and (x2, y2) are two points on the line. The slope tells you the rate of change of the y-values with respect to the x-values.

The y-intercept is the point where the line crosses the y-axis. To find the y-intercept, set x = 0 in the equation y = mx + b and solve for y.

Once you have the slope and the y-intercept, you can plot the y-intercept on the y-axis and then use the slope to find other points on the line. To find another point, use the slope to find the change in y as you change x by 1. For example, if the slope is 2/3, then for every 1 unit increase in x, the y-value increases by 2/3.

By plotting multiple points and connecting them with a straight line, you can graph any linear equation. The graph represents all the points that satisfy the equation.

In this lesson, you will practice graphing linear equations and interpreting graphs to make predictions and solve problems. You will also learn about different forms of linear equations, such as slope-intercept form and point-slope form, and how to convert between them.

Overall, graphing linear equations is an important skill in mathematics and can be useful in a variety of real-world applications, such as analyzing data and predicting trends.