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)