The equation of the line is 45y = -5x - 46
The slope of line is a measure of it's steepness also know as rise over run.
According to the given data
Point (x₁,y₁) is (-5,-1) and point (x₂,y₂) is (4,-2)
A linear equation is of the form y = ax + b.
Where a is the slope and b is the y intercept.
How did we know that it is a linear equation we have been asked find the line through the points and curves can not be linear so it is a line.
Here the slope of the line is a
We know slope is (y₂-y₁)/(x₂-x₁)
∴ a = {-2-(-1)}/{4-(-5)}
a = -1/9.
∴ y = -1/9x + b
Now we will use any of the given set of points for x and y
when x = -5, y = -1
-1 = -1/9(-5) + b
b = - 1/45 - 1
b = -46/5
So, the equation of the line is y = -1/9x - 46/45 or 45y = -5x - 46.
learn more about equation of a line here :
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