The slope of the line passing through the points (x,4) and (4,6) is m=2. What is x?

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Wiggin42's profile pic

Wiggin42 | Student, Undergraduate | (Level 2) Valedictorian

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We know the points (x,4) and (4,6) and that m=2. We want to solve for x. 

Recall that slope is defined as the change in y divided by the change in x. Which can be written as: 

m = (y - y1)/(x - x1)

Solve for x: 

x - x1 = (y - y1)/m 

x = (y - y1)/ m   + x1

x = (4 - 6)/2 + 4

x = -2/2 + 4 = -1 + 4

x = 3

giorgiana1976's profile pic

giorgiana1976 | College Teacher | (Level 3) Valedictorian

Posted on

We'll recall the form of the equation of the line in the standard form:

y = mx + b, where m is the slope and b is y intercept.

We know, from enunciation, that the line has the slope m= 2. We'll substitute the value of the slope in the equation of the line.

y =2x + b

The point (4, 6) lies the line if and only if it's coordinates verify the equation of the line:

6 = 2*4 + b

6 = 8 + b

We'll subtract 6 both sides and we'll apply the symmetric property:

b = 6 - 8

b = -2

The equation of the line is:

y = 2x - 2

The point  (x, 4) lies on the given line if and only if it's coordinates verify the equation of the line.

4 = 2x -  2

We'll add 2 both sides:

2x = 4+2

2x = 6

x = 3

The missing coordinate is x = 3.

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