Question

This exercise emphasizes the "mechanical aspects" of working with linear equations. Find the equation of a line with the following characteristics.

a.) Passing through the points (1, −1) and (−3, 4).

5x + 4y - 1 = 0

(b) Passing through the point (−1, −2) with slope m = 50.

y = 50x + 48

Questions I need answered:

(e) Perpendicular to the line in (a) and passing through (2, 2).

(f) Parallel to the line in (b) and having *y*-intercept
b = −15.

(g) In slope intercept form having the equation 5x + 3y = 7.

(h) Crossing the *x*-axis at x = 4 and having slope m =
1.

Answer #1

This exercise emphasizes the "mechanical aspects" of working
with linear equations. Find the equation of a line with the
following characteristics.
(a) Passing through the points (1, −1) and (−3, 4).
please show your work and explanation. I am having a hard time
with doing the problem step by step! Thank you.

1)Find sets of parametric equations and symmetric equations of
the line that passes through the two points. (For the line, write
the direction numbers as integers.)
(5, 0, 2), (7, 10, 6)
Find sets of parametric equations.
2) Find a set of parametric equations of the line with the given
characteristics. (Enter your answer as a comma-separated list of
equations in terms of x, y, z, and
t.)
The line passes through the point (2, 1, 4) and is parallel to...

find the parametric equation of the line passing through the
point (1,7,2), parallel to the plane x+y+z=2 and perpendicular to
the line x=2t, y=(3t+5)2, and z=(4t-1)/3

17.
Match the information about each graph with the correct linear
equation.
Information
Linear Equations
(a)
The graph of the equation has
y-intercept
(0,−99).
A.
6 x plus y equals negative 96x+y=−9
(b)
The graph of the equation has (0, 0) as x-intercept and
y-intercept.
B.
y equals 4 xy=4x
(c)
The graph of the equation does not have an x-intercept.
C.
y equals 7y=7
(d)
The graph of the equation has
x-intercept
(77,0).
D.
x minus 7 equals 0...

During the period 1990 – 2004 the average commute to work in the
Greater Washington, D.C. area increased from 20 minutes in 1990 (t
= 0) by an average of 3 minutes per year. Use these data to express
y, the average number of minutes commuting to work, as a linear
function of x, the number of years since 1990.
3. Find the equation of each line. Put into
slope-intercept form whenever possible.
(a) The vertical line through...

(a) Write the equation in slope-intercept form.
y = −(x − 5)
(b) Write the equation in slope-intercept form.
y + 2x = 6
A restaurant serves 80 customers per hour.
(a) Write an equation that relates the number of customers
C and time t.
Use the slope and y-intercept to sketch the graph of
each equation.
(a)
y = 3x + 2
Identify the x-intercept.
b)
y = − 1/5x
Identify the x-intercept.
(c)
y = 3/2x-6
Identify the...

Find an equation for each of the following planes. Use x, y and
z as the variables.
a) An equation of the plane passing through the points (1,−1,1),
(0,−2,−1) and (−4,0,6)
b) An equation of the plane consisting of all points that are
equidistant (equally far) from (−3,−5,−1) and (4,−1,−3)
c) An equation of the plane containing the line
x(t)= [0, -1, 1] + t[0, 4, -1] and is
perpendicular to the plane 3y − 4z = −7

a. Determine an equation of the line of intersection of the
planes 4x − 3y − z = 1 and 2x + 4y + z = 5.
b. Find the scalar equation for the plane through (5, −2, 3) and
perpendicular to that line of intersection.

Determine the symmetric and parametric equations of the
line:
(A.) parallel to the z-axis passing through the point (1, 2, 1)
(b.) Parallel to the line (1-2x)/3 = y/4 = (2z + 1)/4 and
passing through the point (2, 1, 0)
(c.) Perpendicular to the straight R defined by r: X = (2,-1, 2)
+ t (1, 2,-1) and passes through Point P (3, 2, 1)

1/ Find linear equation for the plane containing (-1,2,1) that
is parallel to the plane 2x - y + 3z = 1
2/ Find linear equation for the plane containing (2,0,9) that is
perpendicular to the line (x-2)/5 = (y+4)/3 = z/2

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