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2 years ago

What is the slope of a line that is perpendicular to a line whose equation is −2y=3x+7 ?

Mathematics

2 answers:

Salsk061 [2.6K]2 years ago

6 0

Answer:

$\frac{2}{3}$ is the Slope of a line that is perpendicular to a given line equation -2y=3x+7

Step-by-step explanation:

We are given here with the equation of the line $-2y=3x+7$ or we can write this equation as $y=\frac{-3}{2}x+\frac{-7}{2}$

the general equation of the line $y=mx+b$ where m is the slope and b is the y-intercept.

Compare the given equation with general equation we get,

the value of slope(m) $=\frac{-3}{2}$

The slope of line perpendicular to a line is, $m_{perpendicular}=\frac{-1}{m}$

Since, the slope of the given line is, m= $\frac{-3}{2}$

then, $m_{perpendicular}=\frac{-1}{\frac{-3}{2} }$ $=\frac{2}{3}$

Therefore, the slope of a line that is perpendicular to a line whose equation is -2y=3x+7 is, $\frac{2}{3}$

jarptica [38.1K]2 years ago

4 0

The answer is $\frac{2}{3}$

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2 years ago

The hypotenuse of a right triangle is 13.0, and one leg is 9.0 units shorter than the other. Find the dimensions of the figure (

Darina [25.2K]

Let, one leg be x units.
since the other leg is 9.0 units shorter than the other,
the measure of the other leg =x-9
hypotenuse =13.0 units
According to Pythagorean theorem, the square of the hypotenuse is equal to the sum of squares of the other two sides.
x^2 +(x-9)^2 =13^2
x^2 + x^2 -18x +81 = 169
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Divide the whole equation by 2
x^2 - 9x -44 =0
Let's use the quadratic formula to find the roots.
formula: x= [-b Â± sqrt(b^2-4*a*c)]/2*a
a=1 b=-9 c=-44
x= [9Â±sqrt(81+176)]/2
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length of a triangle cannot be negative,
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2 years ago

Why is the equation y-y1=m(x-x1) called the point-slope form?

MatroZZZ [7]

Answer:

The equation of the line with slope m = 2 and passing through the point (1, 1) will be:

$y = 2x$

Step-by-step explanation:

We know that the point-slope form of the line equation is

$y-y_1=m\left(x-x_1\right)$

where

m is the slope of the line

(x₁, y₁) is the point

The formula $y-y_1=m\left(x-x_1\right)$ is termed as the point-slope form of the line equation because if we know one point on a certain line and the slope of that line, then we can easily get the line equation with this formula and, hence, determine all other points on the line.

For example, if we are given the point (1, 1) and slope m = 2

Then substituting the values m = 2 and the point (1, 2)

$y-y_1=m\left(x-x_1\right)$

$y - 2 = 2(x-1)$