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3 years ago

Write the equation of the line that passes through (3, 4) and (2, −1) in slope-intercept form

Mathematics

2 answers:

myrzilka [38]3 years ago

7 0

Answer:

$y = 5x - 11$

Step-by-step explanation:

1) Find slope

2) Substitute 1 point back into formula to find y-intercept, aka c

tresset_1 [31]3 years ago

7 0

ANSWER

$y = 5x - 11$

EXPLANATION

The given line passes through:

(3,4) and (2,-1).

The slope is given by:

$m = \frac{ - 1 - 4}{2 - 3}$

$m = \frac{ - 5}{ - 1} = 5$

The equation can be found using

$y-y_1=m(x-x_1)$

We plug in the point and slope to get:

$y - 4 = 5(x - 3)$

$y - 4 = 5x - 15$

$y = 5x - 15 + 4$

$y = 5x - 11$

This is the slope-intercept form

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The sale price of every item in a store is 75% of its usual price. A. The usual price of a jacket is $80, what is its sale price

riadik2000 [5.3K]

75 × 0.01 = 0.75

0.75 × 80 = $60

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3 years ago

X squared+ y squared = 2 y = 2x squared – 3 Which of the following describes the system?

cluponka [151]

Answer:

$x=-1,1,-\sqrt{\frac{7}{4} },\sqrt{\frac{7}{4}}$ and $y=-1,\frac{1}{2}$

The ordered pair solutions are $(-\sqrt{\frac{7}{4}},0.5)$ , $(\sqrt{\frac{7}{4}},0.5)$ , $(-1,-1)$ , and $(1,-1)$ .

Step-by-step explanation:

I'm assuming the system is $\left \{ {x^2+y^2=2} \atop {y=2x^2-3}} \right.$ :

$x^2+y^2=2$

$x^2+(2x^2-3)^2=2$

$x^2+(4x^4-12x^2+9)=2$

$x^2+4x^4-12x^2+9=2$

$4x^4-11x^2+9=2$

$4x^4-11x^2+7=0$

$x^4-11x^2+28=0$

$(x^2-7)(x^2-4)=0$

$(4x^2-7)(x^2-1)=0$

$4x^2-7=0$

$4x^2=7$

$x^2=\frac{7}{4}$

$x=\pm\sqrt{\frac{7}{4}}$

$x^2-1=0$

$x^2=1$

$x=\pm1$

$y=2x^2-3$

$y=2(\pm\sqrt{\frac{7}{4}})^2-3$

$y=2({\frac{7}{4}})-3$

$y=\frac{7}{2}-3$

$y=\frac{1}{2}$

$y=2x^2-3$

$y=2(\pm1)^2-3$

$y=2(1)-3$

$y=2-3$

$y=-1$

Therefore, $x=-1,1,-\sqrt{\frac{7}{4} },\sqrt{\frac{7}{4}}$ and $y=-1,\frac{1}{2}$

The ordered pair solutions are $(-\sqrt{\frac{7}{4}},0.5)$ , $(\sqrt{\frac{7}{4}},0.5)$ , $(-1,-1)$ , and $(1,-1)$ .

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3 years ago

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Cameron buys 2.45 pounds of apples and 1.65 pounds of pears. Apples and pears each cost c dollars per pound. If the total cost a

nordsb [41]

Answer:

$4.12=2.45c+1.65c$

Step-by-step explanation:

We are given,

Cameron buys 2.45 pounds of apple and 1.65 pounds of pears.

Also, the cost of apples and pears is 'c' dollars per pound.

Thus, the cost of 2.45 pounds of apple is $2.45c$ dollars and the cost of 1.65 pounds of pear is $1.65c$ dollars.

Since, the total cost after using a coupon is $4.12.

So, we get the equation representing the situation is,

Total cost = Total cost of apples + Total cost of pears.

i.e. $4.12=2.45c+1.65c$

i.e. $4.12=4.1c$

i.e. $c=\frac{4.12}{4.1}$

i.e. c = 1 dollar

Hence, the required equation to find c is $4.12=2.45c+1.65c$ .

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