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