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Find the coordinates of the points of intersection of the graphs with coordinate axes:y=−1.5x+3Question
Find the coordinates of the points of intersection of the graph with the coordinate axes.
Y=-1.5x+3
Y=-1.5x+3
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Answered by
GPT-4o mini
To find the points of intersection of the line given by the equation \( y = -1.5x + 3 \) with the coordinate axes, we will find the x-intercept and the y-intercept.
### 1. Finding the y-intercept
The y-intercept occurs where \( x = 0 \).
Substituting \( x = 0 \) into the equation:
\[
y = -1.5(0) + 3 = 3
\]
Thus, the y-intercept is at the point \( (0, 3) \).
### 2. Finding the x-intercept
The x-intercept occurs where \( y = 0 \).
Setting \( y = 0 \) in the equation and solving for \( x \):
\[
0 = -1.5x + 3
\]
Rearranging gives:
\[
1.5x = 3
\]
Dividing by 1.5:
\[
x = \frac{3}{1.5} = 2
\]
Thus, the x-intercept is at the point \( (2, 0) \).
### Summary of Intercepts
- The y-intercept is \( (0, 3) \).
- The x-intercept is \( (2, 0) \).
So, the coordinates of the points of intersection with the axes are:
- \( (0, 3) \) (y-intercept)
- \( (2, 0) \) (x-intercept)
### 1. Finding the y-intercept
The y-intercept occurs where \( x = 0 \).
Substituting \( x = 0 \) into the equation:
\[
y = -1.5(0) + 3 = 3
\]
Thus, the y-intercept is at the point \( (0, 3) \).
### 2. Finding the x-intercept
The x-intercept occurs where \( y = 0 \).
Setting \( y = 0 \) in the equation and solving for \( x \):
\[
0 = -1.5x + 3
\]
Rearranging gives:
\[
1.5x = 3
\]
Dividing by 1.5:
\[
x = \frac{3}{1.5} = 2
\]
Thus, the x-intercept is at the point \( (2, 0) \).
### Summary of Intercepts
- The y-intercept is \( (0, 3) \).
- The x-intercept is \( (2, 0) \).
So, the coordinates of the points of intersection with the axes are:
- \( (0, 3) \) (y-intercept)
- \( (2, 0) \) (x-intercept)
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