A line segment has endpoints P(-3, 2) and Q(x, 5). PQ has a slope of 3. What is the value of x?
(Y2-Y1)/(X2-X1) = m
(5-2)/(x+3) = 3
3x+9 = 3
3 x = -6
x = -2
To find the value of x, we need to use the formula for the slope of a line.
The formula for the slope, m, of a line passing through two points (x1, y1) and (x2, y2) is given by:
m = (y2 - y1) / (x2 - x1)
In this case, one endpoint is P(-3, 2) and the other endpoint is Q(x, 5), and the slope is given as 3.
Let's substitute the coordinates into the slope formula:
3 = (5 - 2) / (x - (-3))
Simplifying the equation gives us:
3 = 3 / (x + 3)
To solve for x, we can cross-multiply:
3(x + 3) = 3
Now we can distribute:
3x + 9 = 3
Next, we can isolate the x term:
3x = 3 - 9
Simplifying:
3x = -6
Finally, to solve for x, we divide both sides of the equation by 3:
x = -6 / 3
Simplifying further:
x = -2
Therefore, the value of x is -2.
To find the value of x, we need to use the slope-intercept form of a line equation, which is y = mx + b, where m represents the slope and b represents the y-intercept.
Given that the line segment PQ has a slope of 3, we can write the equation for the line as: y = 3x + b.
Now, let's substitute the coordinates of point P (-3, 2) into the equation. Since the point P lies on the line, the equation should hold true for these coordinates. Therefore, we have:
2 = 3(-3) + b.
Simplifying the equation, we get:
2 = -9 + b.
To isolate b, let's add 9 to both sides of the equation:
2 + 9 = -9 + b + 9,
11 = b.
Now we know that the y-intercept (b) is equal to 11. Therefore, our equation for the line segment PQ is:
y = 3x + 11.
Next, we need to find the value of x when the y-coordinate is 5 (from the other endpoint Q(x, 5)). We can substitute these values into the equation:
5 = 3x + 11.
To solve for x, let's isolate x by subtracting 11 from both sides of the equation:
5 - 11 = 3x + 11 - 11,
-6 = 3x.
Finally, we can solve for x by dividing both sides of the equation by 3:
-6 / 3 = 3x / 3,
-2 = x.
Therefore, the value of x is -2.