The linear equations for each graph are:
1) y = 2x - 1
2) y = (-4/3)*x - 4
3) y = (1/2)*x + 2
4) y = x + 2
How to find the equations of the lines?
A general linear equation i the slope-intercept form is written as follows:
y = ax + b
Where a is the slope and b is the y-intercept.
For the first line we can see that the y-intercept is y = -1, then:
y = ax - 1
And it passes through (1, 1), then:
1 = a*1 - 1
2 = a
This line is:
y = 2x - 1
2) The y-intercept here is y = -4
y = ax - 4
The line also passes through (-3, 0), replacing that:
0 = -3a - 4
4/-3 = a
This line is:
y = (-4/3)*x - 4
3) The y-intercept here is 2
y = ax + 2
The line also passes through (2, 3), then:
3 = a*2 + 2
3 - 2 = a*2
1/2 = a
The line is y = (1/2)*x + 2
4) The y-intercept is y = 2
y = ax + 2
And the line passes through (1, 3), then:
3 = a*1 + 2
3 - 2 = a
1 = a
y = x + 2