Sure, let's solve this step-by-step.
We are given a point [tex]\((-1, -2)\)[/tex] and a slope [tex]\(2\)[/tex]. We're asked to find the y-intercept of the line passing through this point with the given slope.
1. Understanding slope-intercept form: The equation of a straight line in slope-intercept form is:
[tex]\[
y = mx + b
\][/tex]
where [tex]\(m\)[/tex] is the slope and [tex]\(b\)[/tex] is the y-intercept.
2. Substitute the given slope: We plug the given slope [tex]\(m = 2\)[/tex] into the slope-intercept form:
[tex]\[
y = 2x + b
\][/tex]
3. Use the given point [tex]\((-1, -2)\)[/tex]: Substitute [tex]\(x = -1\)[/tex] and [tex]\(y = -2\)[/tex] into the equation to find [tex]\(b\)[/tex].
[tex]\[
-2 = 2(-1) + b
\][/tex]
4. Solve for [tex]\(b\)[/tex]:
[tex]\[
-2 = -2 + b \\
-2 + 2 = b \\
b = 0
\][/tex]
Thus, the y-intercept [tex]\(b\)[/tex] is [tex]\(0\)[/tex].
So, the y-intercept of the line passing through the point [tex]\((-1, -2)\)[/tex] with a slope of [tex]\(2\)[/tex] is indeed [tex]\(0\)[/tex].
