A line passes through the point (4, –2) and has a slope of One-half.
A coordinate plane.
What is the value of a if the point (–4, a) is also on the line?
A.-6
B.-5
C.5
D.6
The "point-slope" form of the equation of a straight line :
y - y1 = m ( x - x1 )
y = m ( x - x1 ) + y1
In this case:
x1 = 4 , y1 = - 2 , m = 1 / 2
y = m ( x - x1 ) + y1
y = 1 / 2 ( x - 4 ) + ( - 2 )
y = 1 / 2 x - 2 - 2
y = 1 / 2 x - 4
For x = - 4
y = 1 / 2 x - 4
y = 1 / 2 ( - 4 ) - 4
y = - 2 - 4
y = - 6
To find the value of 'a' if the point (-4, a) is also on the line, we need to use the slope-intercept form of a linear equation: y = mx + b.
Given that the slope is 1/2 and the line passes through the point (4, -2), we can substitute these values into the equation to find the value of 'b'.
-2 = (1/2)(4) + b
-2 = 2 + b
b = -4
Now that we have the value of 'b', we can substitute it back into the equation to find the value of 'a'.
a = (1/2)(-4) + b
a = -2 + (-4)
a = -2 - 4
a = -6
Therefore, the value of 'a' if the point (-4, a) is on the line is -6. Hence, the correct answer is A. -6.
To find the value of "a" if the point (–4, a) is on the line, we can use the point-slope form of a linear equation.
The point-slope form is given by: y - y1 = m(x - x1).
where:
- (x1, y1) represents a point on the line (in this case, (4, -2)).
- m represents the slope of the line (given as 1/2).
- (x, y) represents another point on the line (in this case, (-4, a)) that we want to find the value of "a" for.
Substituting the given values into the equation, we get:
a - (-2) = (1/2)(-4 - 4)
Simplifying further:
a + 2 = (1/2)(-8)
a + 2 = -4
a = -4 - 2
a = -6
Therefore, the value of "a" is -6. So, the correct answer is option A: -6.