Remember that the y-intercept is where the function has a value of [tex]x = 0[/tex] and the x-intercept is where the function has a value of [tex]y = 0[/tex]. Thus, to find the x-intercept and y-intercept, we can substitute these values into the equation and solve for the other variable.
x-intercept
Since the x-intecept has a y-value of 0, we can substitute this into the function and solve for [tex]x[/tex].
[tex]0 = -2x - 3[/tex]
[tex]3 = -2x[/tex]
[tex]x = - \dfrac{3}{2}[/tex]
The x-value of the x-intercept is [tex]-\frac{3}{2}[/tex] and the y-value is 0, meaning that the x-intercept has coordinates [tex]\boxed{(-\frac{3}{2}, 0)}[/tex].
y-intercept
Since the y-intercept has a x-value of 0, we can substitute this into the equation and solve for [tex]y[/tex]:
[tex]y = -2(0) - 3[/tex]
[tex]y = -3[/tex]
The y-value of the y-intercept is -3, meaning that the y-intercept of the function is [tex]\boxed{(0, -3)}[/tex].
