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### Course: Algebra (all content)>Unit 3

Lesson 9: Standard form

# Converting from slope-intercept to standard form

We can rewrite an equation in slope-intercept form (y=mx+b) to be in standard form (Ax+By=C) instead. In this example, we rewrite the slope-intercept equation y=2/3x+4/7 in standard form.

## Want to join the conversation?

• In standard form, shouldn't A be non-negative, non-zero?
• Incidentally, there is no restriction on A being zero. Indeed, B and C can also be zero (but not all at the same time). If A is zero then you get the equation By = C, or y = C/B, which is the equation of a straight, horizontal line with y-intercept equal to C/B. If B is zero then you get a straight, vertical line with x-intercept x = C/A, and if C is zero then you get the equation Ax + By = 0 which is a line with gradient -A/B passing through the origin.
• what if your slope intercept form numbers don't have fractions
• It's okay if they don't have fractions. It's still a linear equation.
• What does the m and b stand for in the equation y=mx+b?
• Sal distributed the numbers at to get rid of the fractions. Do you have to do that, or is that optional?
• If you are asked to write the equation in standard form, then you need to get rid of the fractions. Standard form is: Ax + By = C where A, B and C are integers (so no fractions).
• Why is converting the slope-intercept form into a standard form useful?
• Standard form has uses in matrices as well as solving for intercepts, although the y intercept is part of slope intercept form and x-intercept is not too hard to find. If you have a system of equations with one in slope intercept and one in standard, you could convert so that you could do matrices. Matrices help not as much with two variable equations because substitution or elimination are fine, but you need to learn matrices in two variables so that you may be able to do them in 3 or higher variable problems. Maybe there is no great reason for doing it, but it does help your math skills and may prepare you for higher math in the future.
• how do i answer 1/3x+y=8
• At about , Sal multiplies part of the fraction by 21 and divides another part by 21. What is he doing and why?
• my teacher requires us to have 'Ax' be positive. Can anyone help me convert Sal's equation accordingly??
• How would I go about converting a point-slope form equation (i.e `y + 4 = -6(x + 6)`) to standard form?