Answer:
(7) the slope = [tex]\bf\frac{7}{3}[/tex]
(8) k = -8
Step-by-step explanation:
(7)
We can find the slope of line L by using this formula:
[tex]\boxed{slope(m)=\frac{y_2-y_1}{x_2-x_1} }[/tex]
where (x₁, y₁) and (x₂, y₂) are the coordinates of 2 points that lie on the line.
Line L passes through point (0, 0) and point (3, 7), then:
[tex]\begin{aligned}\\m&=\frac{y_2-y_1}{x_2-x_1}\\\\&=\frac{7-0}{3-0}\\\\&=\bf\frac{7}{3} \end{aligned}[/tex]
(8)
The line passes through points (0, 0), (2, 4) and (-4, k), then:
[tex]\begin{aligned}\\m&=m\\\frac{y_2-y_1}{x_2-x_1}&=\frac{y_3-y_1}{x_3-x_1}\\\\\frac{4-0}{2-0} &=\frac{k-0}{-4-0}\\\\2&=\frac{k}{-4} \\\\\bf k&=-8 \end{aligned}[/tex]
