Answer:
[tex]\large\boxed{Q1.\ \text{2 times greater}}\\\\\boxed{Q2.\ J. 3}\\\\\boxed{Q3.\ B. -\dfrac{4}{5}}[/tex]
Step-by-step explanation:
The slope-intercept form of an equation of a line:
[tex]y=mx+b[/tex]
m - slope
b - y-intercept
The formula of a slope:
[tex]m=\dfrac{y_2-y_1}{x_2-x_1}[/tex]
Q1.
We have the equation of a line p in the standard form
[tex]4x-3y=7[/tex]
Convert to the slope-intercept form:
[tex]4x-3y=7[/tex] subtract 3x from both sides
[tex]-3y=-4x+7[/tex] divide both sides by (-3)
[tex]y=\dfrac{4}{3}x-\dfrac{7}{3}[/tex]
The slope [tex]m_1=\dfrac{4}{3}[/tex]
From the table we have the points (4, 3) and (7, 5). Calculate the slope of line q:
[tex]m_2=\dfrac{5-3}{7-4}=\dfrac{2}{3}[/tex]
Divide the slope of p by the slope of q:
[tex]\dfrac{4}{3}:\dfrac{2}{3}=\dfrac{4}{3}\cdot\dfrac{3}{2}=2[/tex]
Q2.
Parallel line have the same slope. Therefore, if we have the equation of the line in the slope-intercept form, then we have the slope:
[tex]y=3x+2\to m=3[/tex]
Q3.
Parallel line have the same slope.
Calculate the slope from given points (-11, 5) and (-6, 1):
[tex]y=\dfrac{1-5}{-6-(-11)}=\dfrac{-4}{-6+11}=\dfrac{-4}{5}=-\dfrac{4}{5}[/tex]
