Question

Find the coordinates of the points of intersection of the graph with the coordinate axes.
Y=-1.5x+3

Answers

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)
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