How to graph a linear equation.

Question

y = 5x - 10

a) Graph the linear equation

b) Identify the slope

c) Identify the x-intercept and y-intercept

Answer 1

Two points determine a line. So, select two points:

(0,-10)

(2,0)

Connect the dots and keep on going in each direction.

The slope is "rise over run"

For a increase of 10 in y, there is an increase of 2 in x. 10/2 = 5

Note: In slope-intercept form of the equation of a line (y=mx+b), m is the slope !

Also, in the slope-intercept form of the equation of a line (y=mx+b), b is the y-intercept (the value of y when x=0). y-intercept is (0,-10)

The x-intercept is the value of x when y=0. We also selected that point. The x-intercept is (2,0).

Answer 2

There are more than one way to graph the linear equation.

Method 1: Thsi method is the most common and can be applied to a lot of other equations to plot.

Step 1: Make a table of the values of x and y. Consider random values of x and find teh corresponding value of y by replacing in the equation y = 5x - 10. When we replace x by 1 in the equation we get. y = 5(0) - 10 or y = 0 - 10 or y = 10. Similarly, take another value of x.. For example if x = 1 (you may take any other value) and replace in the equation y = 5x - 10 we get y = 5(1) - 10 or y = 5 - 10 or y = -5.

X Y

0 -10

1 -5

Step 2. Now, we have two points (0, -10) and (1, -5). We always write the points in a coordiante system with both the x and y values. The left side value inside the parentheses is the x value and the right side value is the corresponding y value. Corresponding y value means the value of y that we got when we replaced the x value in the equation. We'll identify the two points (0,-10) and (1, -5) in the grapg with x and y axes.

Step 3: Connect the two points and that becomes the plot or graph of the linear equation.