Question

40 points, please help with all of them

Answer 1

Answer:

$\large\boxed{Q1.\ \text{2 times greater}}\\\\\boxed{Q2.\ J. 3}\\\\\boxed{Q3.\ B. -\dfrac{4}{5}}$

Step-by-step explanation:

The slope-intercept form of an equation of a line:

$y=mx+b$

m - slope

b - y-intercept

The formula of a slope:

$m=\dfrac{y_2-y_1}{x_2-x_1}$

Q1.

We have the equation of a line p in the standard form

$4x-3y=7$

Convert to the slope-intercept form:

$4x-3y=7$               subtract 3x from both sides

$-3y=-4x+7$              divide both sides by (-3)

$y=\dfrac{4}{3}x-\dfrac{7}{3}$

The slope $m_1=\dfrac{4}{3}$

From the table we have the points (4, 3) and (7, 5). Calculate the slope of line q:

$m_2=\dfrac{5-3}{7-4}=\dfrac{2}{3}$

Divide the slope of p by the slope of q:

$\dfrac{4}{3}:\dfrac{2}{3}=\dfrac{4}{3}\cdot\dfrac{3}{2}=2$

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:

$y=3x+2\to m=3$

Q3.

Parallel line have the same slope.

Calculate the slope from given points (-11, 5) and (-6, 1):

$y=\dfrac{1-5}{-6-(-11)}=\dfrac{-4}{-6+11}=\dfrac{-4}{5}=-\dfrac{4}{5}$