Graph are often used to visualize the relationship between two variables. The graph of a linear function is always a straight line. There are two common approaches to graphing a linear function from its equation: 1) using the slope-intercept form which identifies the slope and y-intercept directly from the equation, and 2) using the x- and y-intercepts which involves substituting values of 0 for x and y to find the two points needed to draw the line. Both approaches are illustrated through examples of graphing different linear equations.

2. Graph are often used to help visualize the relationship between two
variables. The graph of linear function in two variables is always a
straight line.
A. Slope-intercept Form
If we are given the slope-intercept form y=mx t b, we can use the
value of the slope and y-intercept identified by this equation
form.

3. Example 1. y = 2x - 1
y = 2x – 1
slope: 2
y-intercept: -1

4. Example 2. 5x + 3y = 15
5x + 3y = 15
3y = -5x + 15
3𝑦
3
=
−5𝑥+15
3
3y = -
5𝑥
3
+ 5
slope: -
5
3
y-intercept : 5

5. B. Using x and y-intercept
Another approach in graphing linear functions is by using the
x- and y-intercepts. Since we only need two points to graph a line,
the intercepts will be all that we need and the easiest coordinates to
get. To get the two points, we will substitute the value of x and y to
0.

6. Example 1. 2x – 5y = -6
Let y = 0 Let x = 0
2x – 5y = -6
2x – 5(0) = -6
2x – 0 = -6
2x = -6 + 0
2x = -6
2𝑥
2
=
−6
2
x = -3
Thus, x-intercept is (-3, 0)
2x – 5y = -6
2(0) – 5y = -6
0 – 5y = -6
-5y = -6 – 0
-5y = -6
−5𝑦
−5
=
−6
−5
y =
6
5
Thus, y-intercept is (0,
6
5
)

7. Example 2. 3x + 2y = 12
Let y = 0 Let x = 0
3x + 2y = 12
3x + 2(0) = 12
3x + 0 = 12
3x = 12 – 0
3x = 12
x =
12
3
x = 4
Thus, x-intercept is (4,0)
3x + 2y = 12
3(0) + 2y = 12
0 + 2y = 12
2y = 12 – 0
2y = 12
y =
12
2
y = 6
Thus, y-intercept is (0, 6)