To find a solution to the equation y = 3x - 1, we have to replace a variable by a number and compute the other variable.
Assuming x = 0, then
y = 3(0) - 1
y = 0 - 1
y = -1
Then, the point (0, -1) is a solution
Assuming x = 1, then
y = 3(1) - 1
y = 3 - 1
y = 2
Then, the point (1, 2) is a solution
Assuming x = 2, then
y = 3(2) - 1
y = 6 - 1
y = 5
Then, the point (2, 5) is a solution
In the next graph, the solutions and the line are shown
The slope of the line that passes through the points (x1, y1) and (x2, y2) is computed as follows:
[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]Replacing with points (0, -1) and (1,2) we can compute the slope, as follows:
[tex]m=\frac{2-(-1)}{1-0}=3[/tex]