Determine the equation of a line given a graph by finding slope and y-intercept.

I will solve this problem by determining the slope (m) and y-intercept (b) for each of the six lines shown in the graphs, and then writing the equation in the form $y = mx + b$.

I'll work through each graph one by one.

Graph 1

First, look closely:
- The line passes through the points (0, 3) and (2, 0).
- The y-intercept is clearly at (0, 3), so b = 3.
- To find the slope, I'll use the formula: $m = \frac{y_2 - y_1}{x_2 - x_1}$.

Let me calculate the slope using the points (0, 3) and (2, 0):
$m = \frac{0 - 3}{2 - 0} = \frac{-3}{2} = -1.5$

So, the equation is $y = -1.5x + 3$.

Graph 2

First, look closely:
- The line passes through the points (0, -2) and (2, 2).
- The y-intercept is at (0, -2), so b = -2.
- Using the slope formula with points (0, -2) and (2, 2):
$m = \frac{2 - (-2)}{2 - 0} = \frac{4}{2} = 2$

So, the equation is $y = 2x - 2$.

Graph 3

First, look closely:
- The line passes through the points (0, -1) and (2, -3).
- The y-intercept is at (0, -1), so b = -1.
- Using the slope formula with points (0, -1) and (2, -3):
$m = \frac{-3 - (-1)}{2 - 0} = \frac{-2}{2} = -1$

So, the equation is $y = -x - 1$.

Graph 4

First, look closely:
- The line passes through the points (0, -2) and (1, 2).
- The y-intercept is at (0, -2), so b = -2.
- Using the slope formula with points (0, -2) and (1, 2):
$m = \frac{2 - (-2)}{1 - 0} = \frac{4}{1} = 4$

So, the equation is $y = 4x - 2$.

Graph 5

First, look closely:
- The line passes through the points (0, -4) and (2, -7).
- The y-intercept is at (0, -4), so b = -4.
- Using the slope formula with points (0, -4) and (2, -7):
$m = \frac{-7 - (-4)}{2 - 0} = \frac{-3}{2} = -1.5$

So, the equation is $y = -1.5x - 4$.

Graph 6

First, look closely:
- The line passes through the points (0, 1) and (2, 2).
- The y-intercept is at (0, 1), so b = 1.
- Using the slope formula with points (0, 1) and (2, 2):
$m = \frac{2 - 1}{2 - 0} = \frac{1}{2} = 0.5$

So, the equation is $y = 0.5x + 1$.

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Here are the final answers for each graph:

1. Slope: -1.5, y-intercept: 3, Equation: $y = -1.5x + 3$
2. Slope: 2, y-intercept: -2, Equation: $y = 2x - 2$
3. Slope: -1, y-intercept: -1, Equation: $y = -x - 1$
4. Slope: 4, y-intercept: -2, Equation: $y = 4x - 2$
5. Slope: -1.5, y-intercept: -4, Equation: $y = -1.5x - 4$
6. Slope: 0.5, y-intercept: 1, Equation: $y = 0.5x + 1$