Line y = kx + b passes through points A (-1; -9) and B (2; 6) Write the equation of this straight line.
June 15, 2021 | education
| In order to find the coefficients k and b of the straight line y = kx + b, if it passes through points A (-1; -9) and B (2; 6).
Let’s compose and solve the system of equations:
-9 = -k + b;
6 = 2k + b;
We solve the system using the substitution method. Let us express the variable b from the first equation of the system in terms of k.
System:
b = k – 9;
6 = 2k + k – 9.
We solve the second equation of the system:
6 = 2k + k – 9;
6 + 9 = 3k;
3k = 15;
k = 15: 3;
k = 5.
System of equations:
b = k – 9 = 5 – 9 = -4;
k = 5.
We write down the equations of the straight line:
y = 5x – 4.
Answer: y = 5x – 4 equation of a straight line.
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