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erastovalidia [21]
3 years ago
15

The points (4, 9) and (0, 0) fall on a particular line. What is its equation in slope-intercept form?

Mathematics
1 answer:
BlackZzzverrR [31]3 years ago
6 0

Answer:

The equation of the line would be y = 4/9x

Step-by-step explanation:

In order to find the equation, we first need to find the slope. We can do this by using the slope equation with the points.

m(slope) = (y2 - y1)/(x2 - x1)

m = (9 - 0)/(4 - 0)

m = 9/4

Now that we have this, we can use point-slope form along with one of the points to get the equation.

y - y1 = m(x -x1)

y - 0 = 4/9(x - 0)

y = 4/9x

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Answer:

second option

Step-by-step explanation:

The slopes of perpendicular lines have a product of -1. The slope of this line is 3 from the graph so the slope of our line will be -1/3. We know the slope of the line and a point (F, G) that belongs to the line so we can use point-slope form.

Point-slope form: y - y₁ = m(x - x₁) and we know that m = -1/3 and (x₁, y₁) = (F, G) so the answer is y - G = -1/3(x - F).

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I have most of A like the x&y int and vertex I just need to know the equation in graphing form.
Serjik [45]

Step-by-step explanation:

a. y = 2x^2 + 4x + 2\\y = (2x^2 +4x) +2\\y= 2(x^2+2x) + 2\\y = 2(x^2 +2x +1) + 2 - 2\\y = 2(x+1)^2 + 0\\(h,k) = (-1,0)

b. y = -x^2 +2x\\y = -(x^2-2x)\\y = -(x^2-2x+1)+1 \\y = -(x-1)^2+1\\(h,k) = (1,1)

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3 years ago
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3 years ago
Write an equation (a) in slope intercept form and (b) in standard form for the line passing through (1,9) and perpendicular to 3
maxonik [38]

Answer:

\large\boxed{a)\ y=\dfrac{5}{3}x+\dfrac{22}{3}}\\\boxed{b)\ 5x-3y=-22}

Step-by-step explanation:

\text{The slope-intercept form of an equation of a line:}\\\\y=mx+b\\m-slope\\b-y-intercept\\\\\text{Let}\ k:y=m_1x+b_1,\ l:y=m_2x+b_2\\\\l\ \perp\ k\iff m_1m_2=-1\to m_2=-\dfrac{1}{m_1}\\\\l\ \parallel\ k\iff m_1=m_2\\\\=========================\\\\\text{We have the equation of a line in the standard form.}\\\text{Convert it to the slope-intercept form.}\\\\3x+5y=1\qquad\text{subtract}\ 3x\ \text{from both sides}\\\\5y=-3x+1\qquad\text{divide both sides bvy 5}\\\\y=-\dfrac{3}{5}x+\dfrac{1}{5}\to m_1=-\dfrac{3}{5}

a)\\\\y=m_2x+b\\\\m_1=-\dfrac{3}{5}\to m_2=-\dfrac{1}{-\frac{3}{5}}=\dfrac{5}{3}\\\\\text{Put the value of slope and the coordinates of the given point (1, 9)}\\\text{to the equation of a line:}\\\\9=\dfrac{5}{3}(1)+b\\\\9=\dfrac{5}{3}+b\qquad\text{subtract}\ \dfrac{5}{3}\ \text{from both sides}\\\\\dfrac{27}{3}-\dfrac{5}{3}=b\\\\\dfrac{22}{3}=b\\\\\text{Finally:}\\\\y=\dfrac{5}{3}x+\dfrac{22}{3}

b)\\\\\text{The standard form of an equation of a line:}\\\\Ax+By=C\\\\\text{Convert the equation}\ y=\dfrac{5}{3}x+\dfrac{22}{3}\ \text{to the standard form:}\\\\y=\dfrac{5}{3}x+\dfrac{22}{3}\qquad\text{multiply both sides by 3}\\\\3y=5x+22\qquad\text{subtract}\ 5x\ \text{from both sides}\\\\-5x+3y=22\qquad\text{change the signs}\\\\5x-3y=-22

6 0
3 years ago
The volume of the sphere is StartFraction 500 Over 3 EndFractionπ cubic units.
Schach [20]

Answer: 5 units.

Step-by-step explanation:

Hi, to answer this question we have to apply the next formula:

Volume of a sphere: 4/3 x π x r³

Where r is the radius:

Replacing with the values given:

500/3 π= 4/3 ( π) x³

Solving for x (radius)

500/3 π ÷ 4/3 ( π) = x^3

125 = r^3

∛125 = r

r = 5 units

Feel free to ask for more if needed or if you did not understand something.

7 0
3 years ago
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