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2 years ago

Write an equation of the line with slope -2 and passing through (3,1) in slope-intercept form

Mathematics

1 answer:

Vinvika [58]2 years ago

8 0

Answer:

y=-2x+7

Step-by-step explanation:

Hi there!

The form of slope-intercept form is given as y=mx+b, where m is the slope and b is the y intercept

We are given the slope (-2) and a point (3,1)

We can immediately substitute -2 as the slope in the equation

y=-2x+b

Now we need to find b

Because the line will pass through the point (3,1), we can use it to solve for b

Substitute 3 as x and 1 as y

1=-2(3)+b

multiply

1=-6+b

add 6 to both sides to isolate b

7=b

Substitute 7 as b into the equation

The line is <u>y=-2x+7</u>

Hope this helps!

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What number added to 66 is 167

denis-greek [22]

Answer:

101

Step-by-step explanation:

To figure this out, you would do 167 - 66 = 101

101 + 66 = 167

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2 years ago

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Leya [2.2K]

Answer:

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Step-by-step explanation:

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2 years ago

What are the roots of the quadratic equation below 2x^2-5x-1=0

PilotLPTM [1.2K]

Answer:

roots=(5±sqrt(33))/4

Step-by-step explanation:

roots=(-b±sqrt(b^2-4ac))/2a

roots=(-(-5)±sqrt(25+8))/(2*2)

roots=(5±sqrt(33))/4

roots=(5+sqrt(33))/4 and (5-sqrt(33))/4

7 0

2 years ago

Solve the system of equations by substitution. 3/8 x + 1/3 y =17/24 and <br> x + 7y = 8

goblinko [34]

$\left \{ {{ \frac{3}{8}x+ \frac{1}{3}y = \frac{17}{14} } \atop {x+7y=8}} \right.$

To solve this system by substitution, first isolate x in the second equation.

$x+7y=8$
$x+7y-7y=8-7y$
$x=8-7y$

Now, plug this expression ( $8-7y$ ) for x in the top equation to solve for y.

$\frac{3}{8} (8-7y)+ \frac{1}{3} y= \frac{17}{14}$
$3- \frac{21}{8} y+ \frac{1}{3} y= \frac{17}{24}$
$72-63y+8y=17$
$72-55y=17$
$-55y=17-72$
$-55y=-55$
$y=1$

Now that you have y, plug it into the second equation and solve for x.

$x+7y=8$
$x+7(1)=8$
$x+7=8$
$x=1$

Last step is to plug your x- and y-values in to both equations to check your work.

$\frac{3}{8} (1)+ \frac{1}{3} y= \frac{17}{24}$

$\frac{3}{8} * \frac{3}{3} = \frac{9}{24} ; \frac{1}{3} * \frac{8}{8} = \frac{8}{24}$

$\frac{9}{24} + \frac{8}{24} = \frac{17}{24}$ <--True

$1+7(1)=8$
$1+7=8$ <--True

Answer:
$x=1 \\ y=1$

5 0

3 years ago

A board with a length of 15 feet is leaning against a vertical wall at a point that is 12 feet above the ground. The angle that

Ivan

Answer:

In fact, the AB could be calculated in a quickest way, using Pythagorean theorem. In here, we try to use the property of trigonometry to work out AB.

Before applying trigonometry, in this right triangle we can calculate the remaining angle C:

C = 180 - 90 - A = 180 - 90 - 53.13 = 36.87 deg

We can use cosine formula, but here we use the sine formula for the sake of convenience. We have:

sine(angle measure) = ratio of opposite side over hypotenuse

In detail, sineC = AB/BC

Then, we have: AB = BC x sineC = 15 x sin(36.87 deg) = 9.000002 = ~9 ft

Hope this helps!

8 0

2 years ago