Q6.
The slope-intercept form: y = mx + b
m - slope
b - y-intercept
We have: slope m = 3, y-intercept (0, 4) → b= 4
Answer: y = 3x + 4
Q7.
2x + 4y = 4 |subtract 2x from both sides
4y = -2x + 4 |divide both sides by 4
y = -0.5x + 1
Only second graph has y-intercept = 1.
Answer: The second graph.
Q8.
The point-slope form:
[tex]y-y_1=m(x-x_1)\\\\m=\dfrac{y_2-y_1}{x_2-x_1}[/tex]
We have
[tex](-16,\ 8)\to x_1=-16,\ y_1=8\\(4,\ -2)\to x_2=4,\ y_2=-2[/tex]
Substitute:
[tex]m=\dfrac{-2-8}{4-(-16)}=\dfrac{-10}{20}=-\dfrac{1}{2}\\\\y-8=-\dfrac{1}{2}(x-(-16))\\\\y-8=-\dfrac{1}{2}(x+16)[/tex]
Answer: The first equation.
Q9.
It's a vertical line. The equation of a vertical line is x = a, where a is any real number.
Answer: x = -4
