Equation of a Line: Slope Intercept Form

Summary

This math recipe will help you find the equation of a line whose slope and y-intercept are given.

Skill Level

Easy

Time

Approx. 1 min

Ingredients

Slope of the line: m

Y-intercept of the line: c

Method

To find the equation of the line, we’ll use the following:

y = mx + c

Examples

Example 1 Find the equation of a line whose slope is –3 and y-intercept is 4.

Solution To find the equation, we’ll use the above form directly.

y = (–3)x + (4)

⇒ y = –3x + 4

The figure shows the line on the XY plane.

Equation of a Line Slope Form

Example 2 Find the equation of a line whose slope is 2 and y-intercept is –5.

Solution To find the equation, we’ll use the above form directly.

y = (2)x + (–5)

⇒ y = 2x – 5

The figure shows the line on the XY plane.

Equation of a Line Slope Form

Example 3 Find the equation of a line which makes an angle of 45° with the x-axis, and whose y-intercept is –2.

Solution In this case, we’ll first calculate the slope as

m = tan(45°) = 1

Now, to find the equation, we’ll use the above form directly.

y = (1)x + (–2)

⇒ y = x – 2

The figure shows the line on the XY plane.

Equation of a Line Slope Form

Example 4 Find the equation of a line whose slope is –1 and which intersects the y-axis at (0, 4).

Solution In this case, the y-intercept is 4.

Now, to find the equation, we’ll use the above form directly.

y = (–1)x + 4

⇒ y = –x + 4

The figure shows the line on the XY plane.Equation of a Line Slope Form

That’s it for this recipe. Hope you found it helpful.

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