To find the slope and y-intercept of a line represented by the equation of the form ax + by = c, you need to rearrange the equation into the slope-intercept form, which is y = mx + b. In this formula:
- m represents the slope of the line.
- b represents the y-intercept, where the line crosses the y-axis.
Here are the steps to do this:
- Start with the given equation: ax + by = c.
- Isolate by on one side of the equation: by = c – ax.
- Next, divide every term by b (assuming b is not zero) to solve for y:
y = -\frac{a}{b}x + \frac{c}{b}.
In this form:
- The slope m is equal to -\frac{a}{b}.
- The y-intercept b is equal to \frac{c}{b}.
Example: Let’s say you have the equation 2x + 3y = 6:
- Isolate 3y: 3y = 6 – 2x.
- Divide by 3: y = -\frac{2}{3}x + 2.
From this, you can see:
- The slope (m) is -\frac{2}{3}.
- The y-intercept (b) is 2 (which means the line crosses the y-axis at the point (0, 2)).
Now you know how to find the slope and y-intercept for any line given its standard equation!