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