What is the equation of this line in standard form? (-4, -1) & (1/2, 3)

Mathematics

1 answer:

BabaBlast [244]3 years ago

4 0

bearing in mind that standard form for a linear equation means

• all coefficients must be integers, no fractions

• only the constant on the right-hand-side

• all variables on the left-hand-side, sorted

• "x" must not have a negative coefficient

$\bf (\stackrel{x_1}{-4}~,~\stackrel{y_1}{-1})\qquad (\stackrel{x_2}{\frac{1}{2}}~,~\stackrel{y_2}{3}) \\\\\\ \stackrel{slope}{m}\implies \cfrac{\stackrel{rise} {\stackrel{y_2}{3}-\stackrel{y1}{(-1)}}}{\underset{run} {\underset{x_2}{\frac{1}{2}}-\underset{x_1}{(-4)}}}\implies \cfrac{3+1}{\frac{1}{2}+4}\implies \cfrac{4}{~~\frac{9}{2}~~}\implies \cfrac{4}{1}\cdot \cfrac{2}{9}\implies \cfrac{8}{9}$

$\bf \begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-\stackrel{y_1}{(-1)}=\stackrel{m}{\cfrac{8}{9}}[x-\stackrel{x_1}{(-4)}]\implies y+1=\cfrac{8}{9}(x+4) \\\\\\ \stackrel{\textit{multiplying both sides by }\stackrel{LCD}{9}}{9(y+1)=9\left( \cfrac{8}{9}(x+4) \right)}\implies 9y+9=8(x+4)\implies 9y+9=8x+32 \\\\\\ 9y=8x+23\implies -8x+9y=23\implies 8x-9y=-23$

You might be interested in

Determine whether the series is convergent or divergent by expressing sn as a telescoping sum (as in Example 8). [infinity] 6 n2

vekshin1

Answer:

Step-by-step explanation:

given

$\sum\limits^\infty_{n=3}\frac{6}{n^2-1}=\sum\limits^\infty_{n=3}\frac{6}{(n-1)(n+1)}\\\\=\sum\limits^\infty_{n=3}\frac{6}{2}(\frac{1}{n-1}-\frac{1}{n+1})\\\\=\frac{6}{2}\sum\limits^\infty_{n=3}(\frac{1}{n-1}-\frac{1}{n+1})\\\\=3[(\frac{1}{2}-\frac{1}{4})+(\frac{1}{3}-\frac{1}{5})+(\frac{1}{4}-\frac{1}{6})+(\frac{1}{5}-\frac{1}{7})+...]\\\\=3[\frac{1}{2}+\frac{1}{3}]=3[\frac{3+2}{6}]=3[\frac{5}{6}]\\\\=\frac{15}{6}=\frac{5}{3}$

5 0

3 years ago

Need some help with this one.

Verizon [17]

Answer:

x² + 4x + 3

Step-by-step explanation:

to find f(g(x)), substitute x = g(x) into f(x)

f(g(x)) = f(x + 2) = (x + 2)² - 1 = x² + 4x + 4 - 1 = x² + 4x + 3

4 0

3 years ago

Which of the following are valid names for the given polygon

barxatty [35]

B,C and D are correct because all of those choices include letters which are arranged in order from left of right.

5 0

3 years ago

the length of a rectngle is 8/3 times as great as its widthwhat is the width if the length of a rectangle is 24 ft.

laila [671]

L=(8/3)W = 24 ft. Solving for W, we mult. both sides of this eqn by (3/8), obtaining

W = (3/8)(24 ft) = 9 ft (answer)

4 0

3 years ago

Plz help im cheeks at math

Vera_Pavlovna [14]

We have an exponential with a fractional base and a positive exponent, and a positive sign at front. Each time we multiply a fraction between zero and one by itself it gets smaller. So as x increases we'll go to zero. As x decreases it goes to positive infinity, as negative powers are the reciprocals of positive power.

The left end approaches positive infinity and the right end approaches zero.

6 0

3 years ago