Find the coordinates of the points of intersection of the graph with the coordinate axes.

Y=-1.5x+3

1 answer

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)