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3 years ago

A line passes through the points (8, –1) and (–4, 2). What is the y-intercept of this line?

1 answer:

4 0

Y=mx+b
m=slope
b=y intercept

alrighty, find the slope

slope between (x1,y1) and (x2,y2) is (y2-y1)/(x2-x1)

the slope between (8,-1) and (-4,2) is (2-(-1))/(-4-8)=(2+1)/(-12)=3/-12=-1/4

y=(-1/4)x+b
find b
subsitute a point
(8,-1)
x=8 and y=-1
-1=(-1/4)(8)+b
-1=-2+b
1=b

the y intercept is y=1 or the point (0,1)

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Use the given transformation to evaluate the integral. 9 x − 3y 2x − y dA, R where R is the parallelogram enclosed by the lines

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$\displaystyle\iint_R(9x-3y)(2x-y)\,\mathrm dA$

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3 years ago

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write an equation of a line that is perpendicular to the given line and that passes through the given point (4,-6); m=3/5

tresset_1 [31]

Answer:

$y=-\frac{5}{3} x-\frac{42}{5}$

Step-by-step explanation:

Given the slope and another point, simply plug them into the point-slope formula to find your y-intercept.

$y-y1=m(x-x1)\\y-(-6)=\frac{3}{5} (x-4)\\y+6=\frac{3}{5} x-\frac{12}{5} \\y=\frac{3}{5} x-\frac{42}{5}$

Now that we've found your y-intercept, we have the original equation. To find the perpendicular equation, you need the opposite reciprocal of your slope.

To find the 'opposite,' change your slope's sign. Since your slope is positive $\frac{3}{5}$ , the opposite is $-\frac{3}{5}$ .

To find the 'reciprocal,' flip your fraction. This will make your slope $-\frac{5}{3}$ .

Your final equation is:

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