Final answer:
The slope-intercept form y = mx + b is used to describe the slope and y-intercept of a line, where m is the slope and b is the y-intercept. To convert to standard form Ax + By = C, rearrange the equation and ensure A is positive. An example is converting y = 3x + 9 to 3x - y = -9.
Step-by-step explanation:
To write the standard form of a linear equation with a slope and an x-intercept, you first need to understand the slope-intercept form of a linear equation, which is y = mx + b. Here, m represents the slope, which is the rise over the run, and b represents the y-intercept, or the y-coordinate where the line crosses the y-axis. To find the x-intercept, one would set y to 0 and solve for x in the equation. However, a standard form of a linear equation looks like Ax + By = C, where A, B, and C are integers and A should not be negative.
Imagine we have an equation in slope-intercept form such as y = 3x + 9, with a slope of 3 and a y-intercept of 9. To convert this to standard form, we need to move the x term to the left side by subtracting 3x from both sides, which would give us -3x + y = 9. Then to ensure that we have a positive x coefficient, we can multiply the entire equation by -1, resulting in 3x - y = -9, which is now in standard form.