The slope of the line passing through p and q is -3/5. What is the value of x?
P(1,4)
Q(x,1)
formula for slope:
m = (y2 - y1)/(x2 - x1)
where (x1,y1) and (x2,y2) are the points on the line. Substituting,
-3/5 = (4 - 1)/(1 - x)
-3(1-x) = 5(3)
-3 + 3x = 15
3x = 18
x = 6
hope this helps :3
To find the value of x, we need to use the slope-intercept form of a linear equation:
y = mx + b
where m is the slope and b is the y-intercept. Since we are given that the slope of the line passing through P(1,4) and Q(x,1) is -3/5, we can plug in the values to the equation:
1 = (-3/5)x + b
To solve for b, we substitute the coordinates of point P into the equation:
4 = (-3/5)(1) + b
Simplifying further:
4 = -3/5 + b
To get rid of the fraction, we multiply both sides of the equation by 5:
20 = -3 + 5b
To isolate b, we add 3 to both sides:
23 = 5b
Finally, we divide both sides by 5 to solve for b:
23/5 = b
Now that we have the value of b, we can substitute it back into the equation to solve for x:
1 = (-3/5)x + (23/5)
Multiplying through by 5:
5 = -3x + 23
Subtracting 23 from both sides:
-18 = -3x
Dividing both sides by -3:
x = 6
The value of x is 6.
To find the value of x, we can use the slope formula, which states that 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, the two points are P(1, 4) and Q(x, 1). The slope is given as -3/5.
Let's substitute the given values into the slope formula:
-3/5 = (1 - 4) / (x - 1)
Next, we'll simplify the equation:
-3/5 = -3 / (x - 1)
To solve for x, we'll cross-multiply:
-3(x - 1) = -3(5)
Distributing the -3 on the left side:
-3x + 3 = -15
Now, let's isolate x by moving the constant term to the right side:
-3x = -15 - 3
-3x = -18
Finally, divide both sides of the equation by -3 to solve for x:
x = -18 / -3
x = 6
Therefore, the value of x is 6.