The normal form of a line is given by the equation x * cos theta + y * sin theta = p where theta is the angle of the normal line from the positive x-axis and p is the length of the normal line. Converting to normal line form, the equation must first be converted into standard form: 2x + 7y = 4. Then dividing the whole equation by sqrt(a^2 + b^2): sqrt(2^2 + 7^2) = sqrt(53). Hence, the equation becomes 2 / sqrt(53) * x + 7 / sqrt(53) * y = 4 / sqrt(53). Therefore, the length of the normal line is 4 / sqrt(53), and the angle is arctan(7/2) = 74.05 degrees.
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Answer:
.
Step-by-step explanation:
The slope of the line is 2.
The slope is going up from left to right, so it'll be positive to start with. From there you have to do rise over run. That is pretty much how many units up and in towards the slope do you have to go until you find 2 points that are in the center of the line. In this case, the rise over run is 2/1 which equals 2.
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Well I would look up all the steps online but you have to divide like 10 then multiply
Y = 3x + 3
y = x - 1
As you can see, both equations are set to equal y. This means the right sides of each equation are equal, since y is isolated in both equations. So to solve this particular system of equations for x, set the right sides of both equations equal to each other. After you've done that, you can proceed to solve the equation algebraically for the variable, x.
3x + 3 = x - 1
2x + 3 = -1
2x = -4
x = -2
Negative two is the x-value. To find the y-value, substitute -2 for x into either equation and solve algebraically for y.
y = x - 1
y = -2 - 1
y = -3
The final step is to check all work by plugging both x- and y-values back into both equations.
y = 3x + 3
-3 = 3(-2) + 3
-3 = -6 + 3
-3 = -3 -- This is true
y = x - 1
-3 = -2 - 1
-3 = -3 -- This is true.
Answer:
(-2, -3)
