Answer:
The equation of the line is y = -3x + 5 "i.e. negative 3x + 5"
Step-by-step explanation:
Given
Points (2,-1) and (5,-10)
Required
Equation of the line
The equation of a line is usually of the form y = mx + b
where m is the gradient or slope of the line and b is the y intercept.
First, the gradient (m) of the line will be calculated;
[tex]Gradient, m = \frac{y_2 - y_1}{x_2 - x_1}[/tex]
From the given points (2,-1) and (5,-10)
[tex]x_1 = 2; y_1 = -1; x_2 = 5; y_2 = -10[/tex]
By substituting the right values;
[tex]m = \frac{y_2 - y_1}{x_2 - x_1}[/tex] becomes
[tex]m = \frac{-10 - (-1)}{5 - 2}[/tex]
[tex]m = \frac{-10 + 1}{5 - 2}[/tex]
[tex]m = \frac{-9}{3}[/tex]
[tex]m = -3[/tex]
The next step is to calculate the y intercept
Recall that the equation of a line is usually of the form y = mx + b
Substitute [tex]m = -3[/tex] in this equation; we have
y = -3x + b
Make b the subject of formula
b = y + 3x
From the given points (2,-1) and (5,-10)
when x = 2, y = -1
Substitute these values in "b = y + 3x"
b = -1 + 3(2)
b = -1 + 6
b = 5
Also when x = 5, y = -10
Substitute these values in "b = y + 3x"
b = -10 + 3(5)
b = -10+ 15
b = 5
Hence, the y intercept is 5 and the gradient is -3
In other words; b = 5 and m = -3
Substitute these values in y = mx + b
y = -3x + 5
Hence, the equation of the line is y = -3x + 5
