y = ax + b，当x=0.2 时，y=0.595113 , 当x=0.15 时，y=0.45623034 , 求a,b

We have a linear equation \( y = ax + b \) with two points: 

1. When \( x = 0.2 \), \( y = 0.595113 \).
2. When \( x = 0.15 \), \( y = 0.45623034 \).

These points give us two equations to solve for \( a \) and \( b \):

\[
0.595113 = 0.2a + b
\]
\[
0.45623034 = 0.15a + b
\]

Let's solve this system of linear equations. We can use the elimination method by subtracting the second equation from the first:

\[
(0.595113 - 0.45623034) = (0.2 - 0.15)a
\]

Let's calculate the values of \(a\) and \(b\).The solution for the coefficients \( a \) and \( b \) is:

\[
a = 2.7776532, \quad b = 0.03958236
\]

So, the equation of the line is:

\[
y = 2.7776532x + 0.03958236
\]

Would you like more details on this solution or have any questions?

Here are 5 related questions to consider:
1. How would the equation change if we had a different set of points?
2. Can you find the value of \( y \) for a different value of \( x \) using this equation?
3. What is the significance of the slope \( a \) in the context of linear equations?
4. How can you determine if two linear equations are parallel or perpendicular?
5. How would you find the intersection point of this line with another line?

**Tip:** Remember, in a linear equation \( y = ax + b \), \( a \) represents the slope, which indicates how steep the line is, and \( b \) represents the y-intercept, where the line crosses the y-axis.

y = ax + b, 当 x = 0.2 时，y = 0.595113 , 当 x = 0.15 时，y = 0.45623034 , 求 a, b

Learn how to find the slope and intercept (a, b) of a linear equation given two points: (x = 0.2, y = 0.595113) and (x = 0.15, y = 0.45623034). This algebra problem covers solving systems of linear equations using the elimination method. Suitable for students in Grades 9-12.

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