﻿ Graph Using Slope Intercept Form Worksheet | Problems & Solutions Graph Using Slope Intercept Form Worksheet

Graph Using Slope Intercept Form Worksheet
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1.
Find the slope of the line parallel to - 5$x$ + 20$y$ = 25. a. 20 b. $\frac{1}{5}$ c. 2 d. $\frac{1}{4}$

Solution:

Two lines are said to be parallel if they have same slope and different y-intercepts.

The slope intercept form of the equation - 5x + 20y = 25 is y = 1 / 4x + 5 / 4.

The slope of the line - 5x + 20y = 25 is 1 / 4.

So, the slope of the line parallel to - 5x + 20y = 25 is 1 / 4.

2.
Write an equation for the line parallel to $y$ + 3$x$ = 6 and having $y$-intercept 10. a. $x$ = - 3$y$ + 10 b. $y$ = - 3$x$ + 10 c. - 6$x$ + 3$y$ = 10 d. $y$ = 6$x$ + 10

Solution:

Two non-vertical lines are said to be parallel if they have same slope and different y-intercepts.

The slope intercept form of the equation is y = - 3x + 6.

The slope for the line y + 3x = 6 is, m = - 3.
[Compare with y = mx + c.]

The slope of the required line is - 3 and the y-intercept is 10.

So, the equation for the line parallel to y + 3x = 6 and having y-intercept 10 is y = - 3x + 10.

3.
What is the $y$-intercept of the line $y$ = + $\frac{5}{6}$? a. 25 b. - $\frac{4}{5}$ c. $\frac{25}{24}$ d. $\frac{5}{6}$

Solution:

The slope-intercept form of the equation of a line with slope m and y-intercept b is y = mx + b.

y = - 4x5 + 5 / 6
[Given Equation.]

b = 56
[Compare the equation with slope-intercept form equation.]

The y-intercept of the line is 5 / 6.

4.
Which of the following lines are parallel? a. $x$ - 5$y$ - 19 = 0, - $x$ - 5$y$ + 9 = 0 b. $x$ + 5$y$ - 19 = 0, $x$ - 5$y$ + 9 = 0 c. $x$ + 5$y$ - 19 = 0, - $x$ - 5$y$ + 9 = 0 d. $x$ + 5$y$ - 19 = 0, - $x$ + 5$y$ - 9 = 0

Solution:

Two lines which have the same slope and different y-intercepts are called parallel lines.

Write all the sets of equations in the standard slope-intercept form, y = mx + b and verify.

For the lines x + 5y - 19 = 0, - x - 5y + 9 = 0:

x + 5y - 19 = 0

y = - x5 + 195

Slope = - 1 / 5 and y-intercept = 19 / 5
[Compare with y = mx + b.]

- x - 5y + 9 = 0

y = - x5 + 95

Slope = - 1 / 5 and y-intercept = 9 / 5
[Compare with y = mx + b.]

Slopes are same and y-intercepts are different.

So, x + 5y - 19 = 0 and - x - 5y + 9 = 0 are parallel.

5.
Which of the following pairs of lines are parallel? a. - $x$ + + 4 = 0, $x$ - + 5 = 0 b. - $x$ - + 4 = 0, - $x$ + - 5 = 0 c. - $x$ + + 4 = 0, - $x$ - + 5 = 0 d. $x$ + + 4 = 0, $x$ - + 5 = 0

Solution:

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 / 4 y + 4 = 0, x - 7 / 4 y + 5 = 0:

- x + 74 y + 4 = 0

y = 47 x - 167

Slope = 4 / 7 and y-intercept = - 16 / 7
[Compare with y = mx + b.]

x - 74 y + 5 = 0

y = 47 x + 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 / 4 y + 4 = 0 and x - 7 / 4 y + 5 = 0 are parallel.

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.

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.

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 = - 73 x + 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.]

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.]

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 = - 25 x - 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 move 2 units downmove 5 unit right Draw a line through the two points.

Graph of the equation 3x + 5y + 6 = 1 + x matches with Graph 1.