is S(93,83) on the line containing P(-3,-1) and Q(5,6)? why?
To determine if the point S(93, 83) is on the line containing P(-3, -1) and Q(5, 6), we need to check if it satisfies the equation of the line.
The equation of the line passing through two points (x₁, y₁) and (x₂, y₂) is given by the slope-intercept form:
y - y₁ = m(x - x₁)
where m is the slope of the line.
First, let's calculate the slope of the line using the given points P(-3, -1) and Q(5, 6):
m = (y₂ - y₁) / (x₂ - x₁)
= (6 - (-1)) / (5 - (-3))
= 7 / 8
Now that we have the slope, we can substitute the coordinates of point P(-3, -1) into the equation:
y - (-1) = (7/8)(x - (-3))
y + 1 = (7/8)(x + 3)
y + 1 = (7/8)x + (7/8)(3)
y + 1 = (7/8)x + 21/8
Now, we need to check if the coordinates of point S(93, 83) satisfies this equation.
Plug in the x-coordinate (93) and y-coordinate (83) into the equation:
83 + 1 = (7/8)(93) + 21/8
84 = (7/8)(93) + 21/8
By simplifying and evaluating the equation, we get:
84 = 651/8 + 21/8
84 = 672/8
84 = 84
Since both sides of the equation are equal, we can conclude that the point S(93, 83) does lie on the line containing P(-3, -1) and Q(5, 6) because it satisfies the equation of the line.