Question

Please help not sure how to do these

Answer 1

We're given two points and two half lines, aka rays.

Point slope form says the line through (a,b) with slope m is

$y-b = m(x-a)$

We can write that in slope-intercept form:

$y = mx + (b-ma)$

The left line goes two up for every one to the right, that's a slope of 2. It ends at (-1,-3). So that line is:

$y = 2x + (-3 -2(-1)) = 2x-1$

We turn that into the ray we like with the condition $x \le -1$ so it ends at our point.

The right ray has slope 1 and endpoint (1,5). That's $x \ge 1$ with the line

$y= x + (5-1(1))= x+4$

Answer:

$y = 2x-1 \textrm{ if } x \le -1$

$y =x+4 \textrm{ if } x \ge 1$

Answer 2

For the bottom graph slope = 2 and when x = -1 f(x) = -3 so equation is

f(x )= 2x - 1.

{ 2x - 1 ( x <= -1)

f(x) = {

{ x ( x >= 1)