Answer:
-4x + 3y = -5
Step-by-step explanation:
Standard form of line equation:
Ax + By = C
To find the standard form of the line equation, first we find the slope intercept, then we transform it into the standard form.
The slope intercept equation is:
y = ax + b
In which a is the slope and b is the y-intercept.
We are given two points:
(-1,-3) and (2,1)
The slope is the change in y divided by the change in x.
Change in y: 1 - (-3) = 1 + 3 = 4
Change in x: 2 - (-1) = 2 + 1 = 3
Slope: a = 4/3
So
y = (4/3)x + b
It passes through the point (2,1), which means that when x = 2, y = 1. We use this to find b.
y = (4/3)x + b
1 = (4/3)*2 + b
1 = (8/3) + b
b = 1 - (8/3)
b = (3/3) - (8/3)
b = -5/3
So
y = (4/3)x - 5/3
Passing to the standard form:
-(4/3)x + y = -5/3
Multiplying by 3
-4x + 3y = -5
