Please walk me through this math step by step?

Question

To the nearest thenth, find the measure of the acute angle that the given line forms with a horizontal line.

y= 5x +3

Answer 1

Slope is defined as "rise" over "run". In your example, your slope is 5 which means a rise of 5 for every run of 1.

If you draw a right triangle, you would draw it with legs of 5 and 1. The angle you want is opposite the long side. Let's call that angle θ (theta).

Using the mnemonic SOH-CAH-TOA, and given you have the measure of the O(opposite) and A(adjacent) sides of the triangle, you would use T(tangent):

tan(θ) = opposite / adjacent

The opposite leg is 5
The adjacent leg is 1

tan(θ) = 5

Take the arctan (on your calculator it is the tan^-1 button)
of both sides:
θ = arctan(5)

Now use your calculator (in degree mode, I assume). I came out with:
θ ≈ 78.6900675 °

Round this to the nearest tenth:
θ ≈ 78.7°

Answer 2

The line is not horizontal (otherwise it would simply have the form y = k).

Therefore, it makes an angle.

The slope of the line is the rate at which y grows when x grows by 1.

Here, the slope is 5 (from the factor in front of x).

As you can see if you plot points along the line, every time you add 1 to the value of x, the value of y will increase by 5.

At any point where you have a value for x and y, draw a horizontal line. We will call this point (X, Y)

Then add 1 to x to find another point on the line:
This point will be (X+1, Y+5)
X+1 because we added 1 to the value of x (which was X)
and Y+5 because y increases by 5 every time x increases by 1.

If we drop a vertical from the second point, onto the horizontal line we drew through (X, Y) we will form a triangle.

the base of the triangle on the horizontal line, goes from (X, Y) to (X+1, Y); it measures 1.

the height of the triangle on the vertical line, goes from (X+1, Y) to (X+1, Y+%); it measures 5.

The tangent of the angle at (X,Y), where the line crosses the horizontal, is 5

If we call this angle s, then tan(s) = 5

Find the angle (between 0 and pi in radians or between 0 and 90 degrees) for which the tangent is 5.

Answer 3

Standard form of a line is:

y = mx + b

m = slope
b = y- intercept

The slope is the rise over run of the line. It is equal to the tangent of the acute angle that the line forms with horizontal. In this case the slope is 5, so 5 is the tangent of the angle. To find the angle we must take the inverse tangent of 5. This equals about 78.7 degrees.

Answer 4

If you problem looks like this...
Please ignore the dots, they are to keep the picture in alignment. The " / " represents the "given line". sorry that it may be not aligned.
...................../
..................../
.................../
.....angle"Y" / angle"X"
_________/__________

1. Then, y+x=180 degrees (you know that, right?)

2. you also know that, (y=5x+3) you must substitute "y"
(5x+3) + x = 180 degrees

3. Solve the algebra, 6x+3=180
6x=180-3=177
angle x = 177 / 6 = 29.5 degrees
angle y = 180-29.5= 150.5 degrees

So, the solution is that the acute angle, "x" is equal to ...
29.5 degrees.

IF THIS IS NOT WHAT YOU ARE LOOKING FOR, LOOK BELOW.

y=5x+3 is the line's equation.
the slope is "5",
that means that for every rise of 5 there is a run of 1
and we know that a slope of 1 means 45 degrees.
therefore, the equation is...
45+(45/2)+(45/4)+(45/8)+(45/16)= 78 degrees

78 degrees is the ANSWER


Hope this is what you were looking for.
Cheers, Samman :)

Answer 5

Slope is defined as "rise" over "run". In your example, your slope is 5 which means a rise of 5 for every run of 1.

If you draw a right triangle, you would draw it with legs of 5 and 1. The angle you want is opposite the long side. Let's call that angle θ (theta).

Using the mnemonic SOH-CAH-TOA, and given you have the measure of the O(opposite) and A(adjacent) sides of the triangle, you would use T(tangent):

tan(θ) = opposite / adjacent

The opposite leg is 5
The adjacent leg is 1

tan(θ) = 5

Take the arctan of both sides:
θ = arctan(5)

Now use your calculator (in degree mode, I assume). I came out with:
θ ≈ 78.6900675 °

Round this to the nearest tenth:
θ ≈ 78.7°

Answer 6

y = 5x + 3 is in the form y = mx + b

Where m = slope & b = intercept y-axis

So, m = 5 & b = 3

Also, the slope m = tanA ( A being the acute angle the line forms with the x-axis)

So,

A = angtan5

A = 78.7° (using your calculator)

Answer 7

The slope of such a line, that is, the amount of rise for every one unit of increase in x, is the tangent of the angle you seek.

Draw it if you like, on paper or in your head, to see.

So, take the arc tangent of 5 and you get 78.7 degrees. Or 1.4 radians if that is preferred.


Added:

But don't bother with the protractor! That's only as accurate as its manufacture and the creation of the drawing. The mathematical approach above is utterly accurate, dead on, exact, etc.

Answer 8

y intercept is 3, y length is 3
x intercept is -3/5, x length is actually 3/5
using tan (angle) = y / x
tan (angle) = 3 / (3/5) = 5
arctan (tan (angle)) = arctan (5) = 78.7 deg
or you could plot the equation and then take a protractor to find that the angle is just under 80 deg

Answer 9

this mean y=mx+b

which is how you graph it.

first to graph:
the 3 means where the line you are graphing crosses the y axis which is the line going up and down.

then after you make a point on 3...5 means you go up 5 spaces/boxes and over 1 space/box and make a point at the spot you are at...

then connect the 2 points and theres you answer!

Answer 10

y=mx+b
y =y coordinate
m= slope
x=x coordinate
b= y-intercept
y=5x+3
use the rise/run method since the slope is 5 rise 5 on your graph run one (1,5)
the y-intercept is 3 so rise 3 run one
graph as (1,3)

The answer would be graphed as 1,5 and 1,3 then connect the dots