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5x-3y 4 0 1 Slope Intercept Form Perpendicular Calculator

Reviewed by Calculator Editorial Team

This calculator helps you find the slope intercept form of the line 5x-3y=4 and its perpendicular line that passes through the point (0,1). The slope intercept form is written as y = mx + b, where m is the slope and b is the y-intercept.

Introduction

The slope intercept form is a common way to represent linear equations. It shows the relationship between two variables in a straightforward manner. For the equation 5x-3y=4, we can convert it to slope intercept form to better understand its properties.

Additionally, we can find the equation of a line that is perpendicular to the original line and passes through a given point. This is useful in various mathematical and real-world applications, such as finding the optimal path or determining the relationship between two variables.

Formula

Slope Intercept Form

The general form of a linear equation is Ax + By = C. To convert this to slope intercept form (y = mx + b), we solve for y:

y = (-A/B)x + (C/B)

For the equation 5x - 3y = 4:

y = (-5/3)x + (4/3)

Perpendicular Line

The slope of the perpendicular line is the negative reciprocal of the original slope. If the original slope is m, the perpendicular slope is -1/m.

Using the point-slope form, we can find the equation of the perpendicular line:

y - y1 = m(x - x1)

Where (x1, y1) is the given point.

Worked Example

Example Calculation

Given the equation 5x - 3y = 4 and the point (0,1):

  1. Convert to slope intercept form:

    5x - 3y = 4

    -3y = -5x + 4

    y = (5/3)x - 4/3

  2. Find the slope of the perpendicular line:

    Original slope (m) = 5/3

    Perpendicular slope = -3/5

  3. Find the equation of the perpendicular line:

    Using point-slope form: y - 1 = (-3/5)(x - 0)

    y = (-3/5)x + 1

Interpreting Results

The slope intercept form y = mx + b provides several useful pieces of information:

  • The slope (m) indicates the rate of change of y with respect to x.
  • The y-intercept (b) is the value of y when x is 0.

For the perpendicular line, the negative reciprocal slope ensures that the two lines are perpendicular to each other. This property is useful in geometry and algebra for finding lines that intersect at right angles.

FAQ

What is the slope intercept form?

The slope intercept form is a way to write a linear equation in the form y = mx + b, where m is the slope and b is the y-intercept. This form makes it easy to graph the line and understand its properties.

How do I find the perpendicular line?

To find the perpendicular line, first determine the slope of the original line. The slope of the perpendicular line is the negative reciprocal of the original slope. Then, use the point-slope form to find the equation of the perpendicular line.

What does the y-intercept represent?

The y-intercept is the point where the line crosses the y-axis. It is the value of y when x is 0. In the slope intercept form y = mx + b, the y-intercept is represented by the constant term b.