What is the equation in point-slope form of the line passing through (-3, -4) and (0, 2)?
Solution:
Point slope form is used to represent a straight line using its slope and a point on the line. That means, the equation of a line whose slope is 'm' and which passes through a point (x1, y1) is found using the point slope form.
The slope of a line is the change in y-coordinate with respect to the change in x-coordinate of that line.
The equation of the slope is y2 - y1 = m (x2 - x1)
Where m is the slope of the line
The points given are (-3, -4) and (0, 2)
To find the slope,
m = (y2 - y1)/ (x2 - x1)
Substituting the values, we get
m = (2 + 4)/ (0 + 3)
m = 6/3
⇒ m = 2
The equation of a line is y = ax + b
To find the real equation, we have to use one point (0, 2)
2 = a(0) + b
Where a is the slope of the equation
2 = 0 + b
⇒ b = 2
We know, y = ax + b
Substituting the values, we get
y = 2x + 2
Therefore, the equation in point-slope form of the line is y = 2x + 2.
What is the equation in point-slope form of the line passing through (-3, -4) and (0, 2)?
Summary:
The equation in point-slope form of the line passing through (-3, -4) and (0, 2) is y = 2x + 2.
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