We have the next given line equation:
[tex]\frac{x}{3}-\frac{y}{2}=-1[/tex]Now, solve for y to get the slope-intercept form y=mx+b.
[tex]\begin{gathered} -\frac{y}{2}=-1+\frac{x}{3} \\ y=2(-1+\frac{x}{3}) \\ y=\frac{2x}{3}-2 \\ \end{gathered}[/tex]Where -2 represents the point where the line cuts the y-axis.
Hence, Q=(0,-2)
To find the x-intercept, set y=0:
[tex]\begin{gathered} y=\frac{2x}{3}-2 \\ 0=\frac{2x}{3}-2 \\ \text{Solve for x:} \\ 2=\frac{2x}{3} \\ 2\cdot3=2x \\ 6=2x \\ \frac{6}{2}=x \\ x=3 \end{gathered}[/tex]Hence, the P point is (3,0)
Now, the gradient is also called the slope.
The slope equation is given by:
[tex]\begin{gathered} m=\frac{y_2-y_1}{x_2-x_1} \\ \end{gathered}[/tex]We can use the two points that we found before or we can get the slope looking at the slope-intercept form:
y=mx+b
where b represents the y-intercept and m represents the slope.
In this case, we found the next form:
[tex]y=\frac{2}{3}x-2[/tex]Hence, the gradient of the line is 2/3.
