Slope Worksheets - Free Printable

Okay, now I'm examining the third graph on the right. This line has a positive slope and passes through the origin (0, 0), which means its y-intercept is 0. To find the slope, I need another point on the line. I can see it also passes through (2, 3). Using these two points, (0, 0) and (2, 3), the change in y is 3 - 0 = 3, and the change in x is 2 - 0 = 2. So the slope is 3/2. Therefore, the equation for this third line should be y = (3/2)x.

Now that I have analyzed all three graphs, I will summarize the equations for each line.

The problem presented three linear graphs on a coordinate plane. The task is to determine the equation of each line in slope-intercept form, which is $y = mx + b$, where $m$ is the slope and $b$ is the y-intercept.

Here is the solution for each graph:

- First Graph (Left):
- The line crosses the y-axis at the point $(0, -3)$, so the y-intercept ($b$) is $-3$.
- To find the slope ($m$), we can use two points on the line, such as $(0, -3)$ and $(2, 1)$.
- The slope is calculated as: $m = \frac{\text{change in } y}{\text{change in } x} = \frac{1 - (-3)}{2 - 0} = \frac{4}{2} = 2$.
- Therefore, the equation of the first line is $y = 2x - 3$.

- Second Graph (Middle):
- The line crosses the y-axis at the point $(0, -1)$, so the y-intercept ($b$) is $-1$.
- Using two points on the line, such as $(0, -1)$ and $(-2, 1)$, we calculate the slope.
- The slope is: $m = \frac{1 - (-1)}{-2 - 0} = \frac{2}{-2} = -1$.
- Therefore, the equation of the second line is $y = -x - 1$.

- Third Graph (Right):
- The line passes through the origin $(0, 0)$, so the y-intercept ($b$) is $0$.
- Using two points on the line, such as $(0, 0)$ and $(2, 3)$, we calculate the slope.
- The slope is: $m = \frac{3 - 0}{2 - 0} = \frac{3}{2}$.
- Therefore, the equation of the third line is $y = \frac{3}{2}x$.

In summary, the equations for the three lines are:
1. $y = 2x - 3$
2. $y = -x - 1$
3. $y = \frac{3}{2}x$