Find the slope and y-intercept of a line given its equation in the form ax + by = c

To find the slope and y-intercept of a line given its equation in the standard form ax + by = c, we need to rewrite the equation in the slope-intercept form, which is y = mx + b. In this format, m represents the slope, and b represents the y-intercept.

Here are the steps to convert ax + by = c into slope-intercept form:

1. Start with the equation ax + by = c.
2. Isolate by on one side of the equation by subtracting ax from both sides: by = -ax + c.
3. Now, solve for y by dividing every term by b: y = –a/bx + c/b.

From this final equation, we can identify the slope and the y-intercept:

• The slope (m) is -a/b.
• The y-intercept (b) is c/b.

For example, if we have the equation 2x + 3y = 6, we can find the slope and y-intercept as follows:

1. Rearranging the equation: 3y = -2x + 6.
2. Dividing by 3: y = –2/3x + 2.

Thus, the slope is -2/3, and the y-intercept is 2.