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Standard Form to Slope Intercept Form Calculator

Select and put the values accordingly into the calculator to find standard form and slope form of an equation.

To Calculate:

Standard Form: Ax + By + C = 0

Enter A

Enter B

Enter C

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Standard Form to Slope Intercept Form Calculator

The standard form to slope intercept form calculator allows you to determine both standard form and slope form of an equation. You can convert linear equations between their Slope-Intercept Form and Standard Form. So select type of conversion from drop-down menu to convert linear equations between the two forms.

Standard Form of a Linear Equation

The generic form of a linear equation is written in the format given below:

Ax + By = C

Where:

A, B, C = coefficients
x, y = variables

You can convert other forms, such as slope-intercept or point-slope form, into standard form using this calculator.

Slope-Intercept Form of a Linear Equation

The slope-intercept form is written as:

y = mx + c

Where:

m = slope of the line
c = y-intercept

You can also use our Slope Intercept Form Calculator to find the slope-intercept form of any linear equation.

How to Convert Standard Form to Slope-Intercept Form?

In this section, we will be solving a couple of examples for you so that you may not feel any difficulty while doing calculations.

Example #1:

Convert 2x − 9y = 15 into slope-intercept form:

2x - 9y = 15
-9y = -2x + 15
y = (2/9)x - 15/9
y ≈ 0.222x - 1.666

From this:

Slope (m) = 0.222
Y-intercept (c) ≈ -1.666
X-intercept: x = -c/m ≈ 7.5
Percentage slope = 0.222 × 100 ≈ 22.22%
Angle of the line: θ = arctan(m) ≈ 12.51°

Example #2:

Convert y = (1/9)x + 6 into standard form:

$y = (1/9)x + 6$

$- (1/9)x + y = 6$

$-x + 9y = 54$ (Multiply by 9)

x - 9y = -54 (Multiply by -1)

From this:

Slope ($m$): $1/9 \approx 0.111$
Y-intercept ($c$): $6$
X-intercept ($x = -c/m$): $-6 / (1/9) = -54$
Percentage slope: $0.111 \times 100 \approx 11.11\%$
Angle of the line: $\theta = \arctan(m) \approx 6.34^\circ$

FAQs

How does slope-intercept form work?

The slope-intercept form y = mx + c shows the slope of the line (m) and the y-intercept (c). It helps in plotting the line and understanding the linear relationship.

Is slope-intercept form the same as point-slope form?

No. Slope-intercept form is a special case of point-slope form. To convert standard form to point-slope form, first convert it to slope-intercept form, then adjust the equation to the point-slope format.

What is the difference between slope and intercept?

The slope indicates the steepness of the line, while the intercept indicates where the line crosses the x-axis or y-axis. Together, they define the line's behavior.

What is point-slope form?

The general point-slope form of a line is:

y - y₁ = m(x - x₁)

This form is useful for finding the equation of a line passing through a specific point.

References

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