Answer
slope: -3/2
equation of the line: y = (-3/2)x
Step-by-step explanation
The slope, m, of the line that passes through the points (x₁, y₁) and (x₂, y₂) is calculated as follows:
[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]
From the graph, this line passes through the points (0, 0) and (2, -3), then its slope is:
[tex]\begin{gathered} m=\frac{-3-0}{2-0} \\ m=-\frac{3}{2} \end{gathered}[/tex]
Equation of a line in slope-intercept form
[tex]y=mx+b[/tex]
where m is the slope and (0, b) is the y-intercept.
Given that the line intercepts the y-axis at the point (0, 0), then b = 0.
Substituting m = -3/2 and b = 0 into the general equation, the equation of this line is:
[tex]\begin{gathered} y=-\frac{3}{2}x+0 \\ y=-\frac{3}{2}x \end{gathered}[/tex]
