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3 years ago

Please help! find the equation (in terms of x) of the line through the point (-4,3) and (3,-2)

Mathematics

2 answers:

Mars2501 [29]3 years ago

6 0

Answer: y= -5/7 x + 1/7

Step-by-step explanation:

vova2212 [387]3 years ago

5 0

Answer:

$y=-\frac{5}{7} x+\frac{1}{7}$

Step-by-step explanation:

Equation of a line: $y = mx+b$

m is the slope, and b is the y-intercept.

m = $\frac{rise}{run} =\frac{y_{2}-y_{1} }{x_{2}-x_{1} } = \frac{-2-3}{3-(-4)} =-\frac{5}{7}$

Now, we have $y=-\frac{5}{7} x+b$

We can insert one set of points in to solve for b.

We will use the first point (-4, 3):

$3=-\frac{5}{7} (-4)+b$

$\frac{5}{7}* \:4+b=3$

$\frac{20}{7}+b=3$

$b=\frac{1}{7}$ .

Equation: $y=-\frac{5}{7} x+\frac{1}{7}$

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Which value of m satisfies the inequality 170-7m >99?

Shkiper50 [21]

Answer:

$\huge \purple{m < \frac{71}{7} } \\$

Step-by-step explanation:

$170 - 7m > 99$

<u>Move 170 to the right side of the inequality</u>

$- 7m > 99 - 170 \\ - 7m > - 71$

<u>Divide both sides by - 7</u>

$\frac{ - 7m}{ - 7} > \frac{ - 71}{ - 7} \\ m > \frac{71}{7}$

Flip the signs

We have the final answer as

$m < \frac{71}{7} \\$

Hope this helps you

7 0

3 years ago

Read 2 more answers

Can you please factor this x^8-7x^4+12

SashulF [63]

Lol yes I can factor that. $x^{4} -3)(x^{4}-4)$ But, this can be factored further. $( x^{2} -2)( x^{2} +2)( x^{4}-3)$

3 0

3 years ago

You inherit $1000, but spends $8 each day at lunch. How many days until you have $768

schepotkina [342]

Answer:

29 days

Step-by-step explanation:

6 0

2 years ago

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F(x)=2(x+1)^2-2 What is the vertex

Bumek [7]

Answer:

(-1,-2)

Step-by-step explanation:

Let's bring back to memory vertex formula for parabolas.

$y=a(x-h)^{2}+k$

Where (h,k) is the vertex.

In $f(x)=2(x+1)^{2}-2$

The vertex is (-1,-2)

8 0

3 years ago

The equation of a circle is ( x - 3) 2 + ( y + 2) 2 = 25. The point (8, -2) is on the circle.

Shtirlitz [24]

Answer:

x =8 is the equation of the tangent.

Step-by-step explanation:

Here the equation of the given circle is: $(x-3)^{2} + (y+2)^{2} = 25$

Now, comparing it with the general equation of circle: $(x-h)^{2} + (y -k)^{2} = r^2$

we get the central coordinates (h,k) = (3,-2)

So, the slope of the line joining center and (8, -2) = $\frac{-2 -(-2)}{8-3} = \frac{0}{5} = 0$

Since the slope of line = 0, line is parallel to x axis.

Now, as tangent and the line is perpendicular to each other

⇒Slope of the tangent = -1/ slope of the line = $\frac{-1}{0}$

Now, by point slope formula: the equation of the tangent is

(y-y0) = m (x-x0)

or, $(y +2) = \frac{-1}{0} (x -8)$

or x =8 is the equation of the tangent.

8 0

3 years ago