A line passes through the point (2, 3) and has a slope of -2. Which is the equation of the line in point-slope form?
Responses
A 2x + y = 72 x + y = 7
B y = -2x + 7y = -2 x + 7
C y - 3 = -2(x - 2)y - 3 = -2( x - 2)
D y = -12
x + 5y = - 1 2 x + 5
E y + 3 = -2(x + 2)y + 3 = -2( x + 2)
The correct answer is C.
The point-slope form of a linear equation is given by y - y1 = m(x - x1), where (x1, y1) is a point on the line and m is the slope of the line.
In this case, the point (2, 3) lies on the line and the slope is -2. Plugging these values into the point-slope form equation, we get:
y - 3 = -2(x - 2)
This equation is equivalent to option C.
The correct equation of the line in point-slope form is option C: y - 3 = -2(x - 2)
To find the equation of a line given a point and the slope, you can use the point-slope form of the equation, which is:
y - y1 = m(x - x1)
where (x1, y1) represents the coordinates of the given point, and m represents the slope.
In this case, the given point is (2, 3) and the slope is -2.
Substituting these values into the point-slope form, we get:
y - 3 = -2(x - 2)
Expanding the equation, we have:
y - 3 = -2x + 4
Now, we can rearrange the equation to put it in the slope-intercept form, y = mx + b, where b represents the y-intercept:
y = -2x + 7
Therefore, the equation of the line in point-slope form is:
C. y - 3 = -2(x - 2)