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satela [25.4K]
2 years ago
7

What is the equation of the line that passes through the point (-4, 2) and has a slope of -5/4?​

Mathematics
1 answer:
gulaghasi [49]2 years ago
6 0

Answer:

y = -5/4 x - 3   is the slope-intercept form

5x + 4y = -12    is the standard form

Step-by-step explanation:

Use the point-slope form:  y - y_{1} = m(x - x_{1})

(x_{1}, y_{1}) = (-4, 2)

y - 2 = -5/4(x + 4)       Multiply by 4 to remove the fraction

4y - 8 = -5(x + 4)

4y - 8 = -5x - 20

4y = -5x - 12

y = -5/4 x - 3   is the slope-intercept form

5x + 4y = -12    is the standard form

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What is an equation of the line that is perpendicular to −x+2y=4 and passes through the point (−2, 1) ?
Elza [17]

Answer:

y=-2x-3

Step-by-step explanation:

Since our equation is in standard form Ax+By=C we must first manipulate the equation so that we have it in the slope-intercept form such that y=mx+b.  Therefore:

-x+2y=4\\2y=x+4\\\\y=\frac{x+4}{2}\\\\y=\frac{1}{2}x+2

Therefore, our slope is 1/2 and our y-intercept is 2.  Now in order to determine a perpendicular line to the one stated above we must then get the negative inverse of our slope meaning \frac{1}{2}=-2 (negative reciprocal).  Now we must use the point slope formula:

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Where m is the slope, x1 is -2 and y1 is 1 (because of the ordered pair given). And so:

y=-2(x-(-2))+1\\\\y=-2(x+2)+1\\\\y=-2x-4+1\\\\y=-2x-3

Therefore, the line that is perpendicular to -x+2y=4 is y=-2x-3.


6 0
3 years ago
Determine the number of x-intercepts that appear on a graph of each function. f (x) = (x - 6)2(x + 2)2
Tpy6a [65]
<span>The number of x-intercepts that appear on the graph of  the function
</span>f(x)=(x-6)^2(x+2)^2 is two (2): x=6 (multiplicity 2) and x=-2 (multiplicity 2)


Solution
x-intercepts:
f(x)=0→(x-6)^2 (x+2)^2 =0

Using that: If a . b =0→a=0 or b=0; with a=(x-6)^2 and b=(x+2)^2

(x-6)^2=0
Solving for x. Square root both sides of the equation:
sqrt[ (x-6)^2] = sqrt(0)→x-6=0
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x-6+6=0+6→x=6 Multiplicity 2

(x+2)^2=0
Solving for x. Square root both sides of the equation:
sqrt[ (x+2)^2] = sqrt(0)→x+2=0
Subtracting 2 both sides of the equation:
x+2-2=0-2→x=-2 Multiplicity 2
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If y varies directly as x and y-21 when x<br> is 7, find x when y = -5.
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