the points are (2.1, -6.3) (-2.5, 4.7)
y=mx+b
find what m= and what b =
I will be happy to critique your thinking.
i got m=-2.39 but the I tried to plug the coordinates into y=mx+b but keep getting two different answers of -1.281 and -1.275.
To find the values of m and b in the equation y = mx + b, you can use the given points (2.1, -6.3) and (-2.5, 4.7) and solve for m and b simultaneously.
Step 1: Start with the general form of the equation: y = mx + b.
Step 2: Substitute the x and y values from one of the points (let's choose the first point, (2.1, -6.3)) into the equation:
-6.3 = m(2.1) + b.
Step 3: Simplify the equation:
-6.3 = 2.1m + b.
Step 4: Repeat the same process for the second point (-2.5, 4.7):
4.7 = m(-2.5) + b.
Step 5: Simplify the equation:
4.7 = -2.5m + b.
Now you have a system of two equations:
-6.3 = 2.1m + b,
4.7 = -2.5m + b.
To solve the system, you can use any method you prefer, such as substitution or elimination. Let's use the substitution method to solve for m and b:
Step 6: Solve one equation for one variable in terms of the other variable:
b = -2.1m - 6.3.
Step 7: Substitute the expression for b into the other equation:
4.7 = -2.5m + (-2.1m - 6.3).
Step 8: Simplify and solve for m:
4.7 = -4.6m - 6.3.
Step 9: Rearrange the equation:
4.6m = -4.7 - 6.3,
4.6m = -11.
Step 10: Divide both sides by 4.6 to isolate m:
m = -11 / 4.6.
Step 11: Calculate m:
m ≈ -2.3913.
Step 12: Substitute the value of m back into equation 1 to solve for b:
-6.3 = 2.1(-2.3913) + b.
Step 13: Simplify and solve for b:
-6.3 = -5.021 + b,
b = -6.3 + 5.021,
b ≈ -1.279.
So, the values of m and b in the equation y = mx + b are approximately:
m ≈ -2.3913 and b ≈ -1.279.