What is the equation of a line parallel to Y=-3x+5 that passes through point (6,8)?
1 answer:
9514 1404 393
Answer:
y = -3x +26
Step-by-step explanation:
We assume the given line is ...
y = -3x +5
This is in slope-intercept form:
y = mx +b
where m = -3 and b = 5.
The parameter m represents the slope of the line. A parallel line will have the same slope, so will be of the form ...
y = -3x +b
We can find the value of b using the given point:
8 = -3(6) +b
26 = b . . . . . . add 18
So, the equation of the parallel line through (6, 8) is ...
y = -3x +26
You might be interested in
Answer:
or
Step-by-step explanation:
-7,-3,1,5,... is a arithmetic sequence.
Arithmetic sequences have a common difference. That is, it is going up by 4 each time.
When you see arithmetic sequence, you should think linear equation.
The point-slope form of a line is .
m is the common difference, the slope.
Any they are using the point at x=1 in the point slope form. So they are using (1,-7).
So let's put this into our point-slope form:
Subtract 7 on both sides:
So your answer is
The answer is A, 
. This is because when plugging in -2 for x, the expression will look like this: 
. To make the exponent positive, you have to flip it into a fraction. Then it will be 
. Lastly, you simplify the denominator into 81.
The roots of an equation are simply the x-intercepts of the equation.
See below for the proof that has at least two real roots
The equation is given as:
There are several ways to show that an equation has real roots, one of these ways is by using graphs.
See attachment for the graph of
Next, we count the x-intercepts of the graph (i.e. the points where the equation crosses the x-axis)
From the attached graph, we can see that crosses the x-axis at approximately <em>-2000 and 2000 </em>between the domain -2500 and 2500
This means that has at least two real roots
Read more about roots of an equation at:
Answer:
This linear system has one solution.
Step-by-step explanation:
First equation: y = x + 2
Second equation: 6x - 4y = -10
Let's change the second equation in slope-intercept form y = mx + b.
<u>Slope-intercept form</u>
y = mx + b
m ... slope
b ... y-intercept
If two lines have the <em>same slope </em>but <em>different y-intercept</em>, they are parallel - <u>system has no solutions</u>.
If two lines have the <em>same slope</em> and the <em>same y-intercept</em>, they are the same line and are intersecting in infinite many points - <u>system has infinite many solutions</u>.
If two lines have <em>different slopes</em> then they intersect in one point - <u>system has one solution</u>.
We see that lines have different slopes. First line has slope 1 and the other line has slope . So the system has one solution.
You can also check this by solving the system.
Substitute y in second equation with y from first.
6x - 4y = -10
6x - 4(x + 2) = -10
Solve for x.
6x - 4x - 8 = -10
2x = -2
x = -1
y = x + 2
y = -1 + 2
y = 1
The lines intersect in point (-1, 1). <-- one solution