Equation of a line given the gradient and point

Equation of a Line Given the Gradient and Point

Introduction

• An equation of a line can be written in many forms, some of the most common are slope-intercept form and point-slope form.
• These equations provide a relationship linking all points on a line and are used extensively in coordinate geometry and algebra.

Slope-Intercept Form

• The slope-intercept form of a linear equation is given as: y = mx + c.
• In this format, m is the gradient of the line and c is the y-intercept.

Point-Slope Form

• One way to write the equation of a line is the point-slope form: y - y1 = m(x - x1).
• In this format, m is the gradient of the line, and (x1, y1) is a specific point known to be on the line.

Finding the Equation of a Line

• To find an equation of a line when given the gradient m and a point on the line (x1, y1), one can use the point-slope form.
• Substituting the known values into the point-slope form will provide an equation representing all points on the line.

Examples

• For example, if the gradient of a line is 2 and it passes through the point (3,4), we can substitute these values into the point-slope form: y - 4 = 2(x - 3).
• Simplifying will give us the slope-intercept form: y = 2x + 2.

Conclusion

• Understanding how to form an equation for a line when given the gradient and a point is vital in algebra and can be applied to other areas of maths as well.
• Regular practice in writing these equations can boost your confidence and accuracy when dealing with problems involving coordinate geometry.