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A line can be formed by at least two known data points. When these two are given, you can connect them and extend infinitely in one direction for both ends. So, that is how we're going to approach the problem. The two points that can be easily determined are the x- and y-intercepts. These are the points which the line intersects on the x- and y-axis, respectively. If we want to find for the x-intercept, just let y=0 and substitute it to the linear equation. Then, we can solve for x. The same thing is done to calculate for the y-intercept.
Solving for the x-intercept: let y=0
-3x + 5y = 6
-3x + 0 = 6
-3x = 6
x = 6/-3
x = -2
Solving for the y-intercept: let x=0
-3x + 5y = 6
-3(0) + 5y = 6
5y = 6
y = 6/5
y = 1.2
So, the two points are (-2,0) and (0,1.2). The line drawn is shown in the picture. This is the graph of the linear equation given.
Solving for the x-intercept: let y=0
-3x + 5y = 6
-3x + 0 = 6
-3x = 6
x = 6/-3
x = -2
Solving for the y-intercept: let x=0
-3x + 5y = 6
-3(0) + 5y = 6
5y = 6
y = 6/5
y = 1.2
So, the two points are (-2,0) and (0,1.2). The line drawn is shown in the picture. This is the graph of the linear equation given.