Need help with writing an equation of the line that passes through the given points.
f(4)=-8, f(-3)=1
when x = 4, y = -8
when x = -3 , y = 1
so as y goes up 9 from -8 to +1
x goes down 7 from 4 to -3
so slope = 9/-7 = -9/7
so it is of form
y = (-9/7) x + b
to find b, use one of those points
when x = -3, y = 1 is easy
1 = (-9/7) (-3) + b
1 = 27/7 + b
b = 7/7 -27/7 = -20/7
so in he end
y = (-9/7) x -20/7
or
7 y = -9 x -20
or
9 x + 7 y = 20
9 x + 7 y = -20
To find the equation of the line that passes through the given points, you can use the point-slope form of a linear equation. This form of the equation is:
y - y1 = m(x - x1)
Where (x1, y1) represents one of the given points on the line, and m represents the slope of the line.
Let's start by finding the slope (m) using the given points. The slope between two points (x1, y1) and (x2, y2) is given by the formula:
m = (y2 - y1) / (x2 - x1)
Using the points (4, -8) and (-3, 1), we can substitute these values into the formula and calculate the slope:
m = (1 - (-8)) / (-3 - 4)
m = 9 / (-7)
Now that we have the slope (m), we can choose any of the given points and substitute its coordinates into the point-slope form equation to find the equation of the line.
Let's use the point (4, -8):
y - (-8) = (9 / (-7))(x - 4)
Simplifying this equation will give us the final equation of the line.