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liberstina [14]
3 years ago
10

Write the equation of the line that passes through the points (−3, 5) and (2, -10) in slope-intercept form.​

Mathematics
1 answer:
schepotkina [342]3 years ago
3 0

Answer:

y=-3x-4

Step-by-step explanation:

Hi there!

Slope intercept form: y=mx+b where m is the slope and b is the y-intercept (the value of y when the line crosses the y-axis)

<u>1) Determine the slope (m)</u>

m=\frac{y_2-y_1}{x_2-x_1} where the two given points are (x_1,y_1) and (x_2,y_2)

Plug in the given points (−3, 5) and (2, -10)

m=\frac{-10-5}{2-(-3)}\\m=\frac{-10-5}{2+3}\\m=\frac{-15}{5}\\m=-3

Therefore, the slope is -3. Plug -3 into y=mx+b as m:

y=-3x+b

<u>2) Determine the y-intercept (b)</u>

y=-3x+b

Plug one of the given points, (−3, 5) or (2, -10) into the equation and isolate b

5=-3(-3)+b\\5=9+b

Subtract 9 from both sides

5-9=9+b-9\\-4=b

Therefore, the y-intercept is -4. Plug -4 into y=-3x+b as b:

y=-3x-4

I hope this helps!

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Lines a and b are parallel.<br><br><br><br> What is the measure of angle m?
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Answer: 55 degrees

Step-by-step explanation:

180-125=55

125 and m make a half a turn which equals 180

4 0
4 years ago
Jamya is making a rectangular blanket. The length of the blanket is 10inches greater than it's worth, W, in inches. Write the fu
natta225 [31]

Answer: (w² + 10)inches²

Step-by-step explanation:

Since the width of the rectangular blanket is given as w and the length of the blanket is 10inches greater than it's width, therefore the length will be:

= 10 + w.

Therefore,

length = 10 + w

width = w

Area = length × width

Area = (10 + w) × w

Area = 10w + w²

Therefore, the area of the blanket will be (w² + 10)inches².

3 0
3 years ago
Help please!posted picture of question
Evgen [1.6K]
The region is in the first quadrant, and the axis are continuous lines, then x>=0 and y>=0
The region from x=0 to x=1 is below a dashed line that goes through the points:
P1=(0,2)=(x1,y1)→x1=0, y1=2
P2=(1,3)=(x2,y2)→x2=1, y2=3
We can find the equation of this line using the point-slope equation:
y-y1=m(x-x1)
m=(y2-y1)/(x2-x1)
m=(3-2)/(1-0)
m=1/1
m=1
y-2=1(x-0)
y-2=1(x)
y-2=x
y-2+2=x+2
y=x+2
The region is below this line, and the line is dashed, then the region from x=0 to x=1 is:
y<x+2 (Options A or B)

The region from x=2 to x=4 is below the line that goes through the points:
P2=(1,3)=(x2,y2)→x2=1, y2=3
P3=(4,0)=(x3,y3)→x3=4, y3=0
We can find the equation of this line using the point-slope equation:
y-y3=m(x-x3)
m=(y3-y2)/(x3-x2)
m=(0-3)/(4-1)
m=(-3)/3
m=-1
y-0=-1(x-4)
y=-x+4
The region is below this line, and the line is continuos, then the region from x=1 to x=4 is:
y<=-x+2 (Option B)

Answer: The system of inequalities would produce the region indicated on the graph is Option B

8 0
3 years ago
There are 2.54 centimeters in 1 inch. There are 100 centimeters in 1 meter.
Alika [10]

Answer:

5 meters

Step-by-step explanation:

If in 1 inch have 2.54 centimeters, in 197 inches will have:

197×2.54 = 500.38 centimeters

If 100 centimeters are 1 meter, 500 centimeters will have 5 meters, so 197 inches have 5 meters

3 0
3 years ago
[20 pts] evaluate the logarithm log(6)1/36​, show work pls!
Delvig [45]

Answer:

\large\boxed{\log_6\dfrac{1}{36}=-2}

Step-by-step explanation:

\text{We know:}\\\\\log_ab=c\iff a^c=b\\\\\log_6\dfrac{1}{36}\qquad\text{use}\ a^{-1}=\dfrac{1}{a}\\\\=\log_636^{-1}=\log_6(6^2)^{-1}\qquad\text{use}\ (a^n)^m=a^{nm}\\\\=\log_66^{(2)(-1)}=\log_66^{-2}\qquad\text{use}\log_ab^n=n\log_ab\\\\=-2\log_66\qquad\text{use}\ \log_aa=1\\\\=-2(1)=-2

\log_6\dfrac{1}{36}=-2\ \text{because}\ 6^{-2}=\dfrac{1}{6^2}=\dfrac{1}{36}

8 0
3 years ago
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