Slope-intercept form:
y=mx+b
m=slope
b=intercept form
Given two points (x₁,y₁) and (x₂,y₂), the slope of the line passes through these points will be:
m=(y₂-y₁)/(x₂-x₁)
In this case, the points are (1,5) and (-2,14), then the slope will be:
m=(14-5)/(-2-1)=9/(-3)=-3
therefore, the equation will be:
y=-3x+b
we need to know the value of b; Therefore, we can use any known point of this line [ (1,5) or (-2,14)] . The result will be the same.
For example:
Point (1,5); ⇒ when x=1; then y=5
y=mx+b
5=-3(1)+b
5=-3+b
b=5+3
b=8
Now, we know the slope (m=-3) and y-intercept (b=8), therefore the equation of this line will be.
y=-3x+8
Answer: y=-3x+8
