What is the value of x in the equation 4x – 2(x + 3) = 8? Show ALL steps in the space below:
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The value of r so the line that passes through (-5,2) and (3,r) has a slope of -1/2 is -2
<u>Solution:</u>
Given that line is passing through point (-5, 2) and (3, r)
Slope of the line is
Need to determine value of r.
Slope of a line passing through point is given by following formula:
--- eqn 1
On substituting the given value in (1) we get
Hence the value of "r" is -2
The geometrical relationships between the straight lines AB and CD is that they are parallel to each other
<h3>How to determine the relationship</h3>It is important to note the following;
- A drawn from the origin and passes through point A (a , b), then the equation of OA = ax + by
- If a line is drawn from the origin and passes through point B (c , d), then the equation of OB = cx + dy
We find the equation of AB by subtracting OB from OA, thus AB = (c - a)x + (d - b)y
The slope of line AB =
⇒ OA= 2 x + 9 y
⇒ OA = 4 x + 8 y
⇒AB = OB - OA
⇒AB = (4 x + 8 y) - (2 x + 9 y)
⇒ AB = 4 x + 8 y - 2 x - 9 y
Collect like terms
⇒ AB = (4 x - 2 x) + (8 y - 9 y)
⇒AB = 2 x + -y
⇒ AB = 2 x - y
⇒ Coefficient of x = 2
⇒ Coefficient of y = -1
⇒ The slope of ab = = 2
For CD
⇒ CD = 4 x - 2 y
⇒Coefficient of x = -4
⇒ Coefficient of y = -2
⇒The slope of cd = = 2
Note that Parallel lines have same slopes
And Slope of ab = slope of cd
AB // CD
Therefore, the geometrical relationships between the straight lines AB and CD is that they are parallel to each other
Learn more about parallel lines here:
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