Two lines which have same slope and different y-intercepts, are said to be parallel.
Write all the sets of equations in the standard slope-intercept form, y = mx + b and verify.
For the lines - x + 7 / 4y + 4 = 0, x - 7 / 4y + 5 = 0:
- x + 74y + 4 = 0
y = 47x - 167
Slope = 4 / 7 and y-intercept = - 16 / 7 [Compare with y = mx + b.]
x - 74y + 5 = 0
y = 47x + 207
Slope = 4 / 7 and y-intercept = 20 / 7 [Compare with y = mx + b.]
Slopes are same and y-intercepts are different.
So, - x + 7 / 4y + 4 = 0 and x - 7 / 4y + 5 = 0 are parallel.
Correct answer : (1)
6.
In the slope-intercept form $y$ = $\mathrm{mx}$ + $b$,$m$ is ______ and $b$ is ______.
a.
$y$-intercept, slope
b.
$x$-intercept, slope
c.
slope, $x$-intercept
d.
slope, $y$-intercept
Solution:
The equation of the line in slope-intercept form is y = mx + b, where m is the slope and b is the y-intercept.
Correct answer : (4)
7.
Find the slope of the graph of the equation $y$ = $\frac{2}{3}$$x$ + $\frac{2}{5}$.
a.
$\frac{2}{5}$
b.
- $\frac{2}{3}$
c.
$\frac{4}{5}$
d.
$\frac{2}{3}$
Solution:
The slope-intercept form of the equation of a line with slope m and y-intercept b is y = mx + b.
y = 23x + 25 [Given Equation.]
m = 23 [Compare the equation with slope-intercept form equation.]
The slope of the line is 2 / 3.
Correct answer : (4)
8.
Find the slope ($m$) and $y$-intercept ($b$) of the graph of the equation 7$x$ + 3$y$ = 14.
a.
$m$ = $\frac{7}{3}$, $b$ = - $\frac{14}{3}$
b.
$m$ = - $\frac{7}{3}$, $b$ = $\frac{14}{3}$
c.
$m$ = $\frac{7}{3}$, $b$ = $\frac{14}{3}$
d.
$m$ = 7, $b$ = 14
Solution:
7x + 3y = 14 [Write original equation.]
3y = - 7x + 14 [Subtract 7x from each side.]
y = - 73x + 143 [Divide each side by 3.]
The equation is in slope-intercept form y = mx + b
The slope is - 73 and y-intercept is 143. [ m = - 73, b = 143.]
Correct answer : (2)
9.
A Painting exhibition is being organized in Redfield. The painters who wish to exhibit and sell their paintings need to pay $100 for the space and $20 for each painting they sell. The equation 20$x$ - $y$ + 100 = 0 models the above situation, where $y$ is the total amount paid to the organizers and $x$ is the number of paintings each painter sells. What is the $y$-intercept of this model? Interprete the meaning of $y$-intercept.
a.
20; charge for each paint sold
b.
- 100; space charge for exhibiting the paints
c.
20$x$ + 100; charge for each paint sold
d.
100; space charge for exhibiting the paints
Solution:
20x - y + 100 = 0
20x + 100 = y [Rearrange the terms.]
The equation is in slope-intercept form y = mx + b, where y - intercept is b.
y-intercept is 100, which is the space charge for exhibiting the paints. [b = 100.]
Correct answer : (4)
10.
Which graph represents the equation 3$x$ + 5$y$ + 6 = 1 + $x$?
a.
Graph 3
b.
Graph 4
c.
Graph 2
d.
Graph 1
Solution:
3x + 5y + 6 = 1 + x [Write original equation.]
5y = - 2x - 5 [Subtract 3x + 6 from each side.]
y = - 25x - 1 [Divide each side by 5.]
The equation is in slope-intercept form y = mx + b.
The slope is - 25 and y-intercept is - 1. [m = - 25, b = - 1.]
Plot the point (0, b) when b is - 1.
Use the slope to locate a second point on line.
m = -25 = riserun→move2unitsdownmove5unitright
Draw a line through the two points.
Graph of the equation 3x + 5y + 6 = 1 + x matches with Graph 1.