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3 years ago

Find an equation for the line that passes through the points (-4, -1) and (6, 3)

Mathematics

2 answers:

Anarel [89]3 years ago

5 0

Answer:

y = (2/5)x + 3/5

Step-by-step explanation:

Points to remember

Equation of the line passing through the poits (x1, y1) and (x2, y2) and slope m is given by

(y - y1)/(x - x1) = m where slope m = (y2 - y1)/(x2 - x1)

To find the slope of line 

Here (x1, y1) = (-4, -1) and (x2, y2) = (6, 3)

Slope = (y2 - y1)/(x2 - x1)

= (3 - -1)/(6 - -4)

= 4/10 = 2/5

To find the equation 

(y - y1)/(x - x1) = m

(y - -1)/(x - -4) = 2/5

(y + 1)/(x + 4) = 2/5

5(y + 1) = 2(x + 4)

5y + 5 = 2x + 8

5y = 2x + 3

y = (2/5)x + 3/5

skad [1K]3 years ago

3 0

Answer:

y=2/5x+3/5

Step-by-step explanation:

Use the slope formula to get the slope:

m=4/10

m=2/5

The y intercept is 3/5

The equation is y=2/5x+3/5

You might be interested in

The variable expression 8=n

Alla [95]

Answer:

The product of 8 and n

3 0

3 years ago

At age 16, Estelle weighed 110lbs.

Cloud [144]

Answer:

Her weight is increase by 18 lbs over past five years and the slope is 3.6 lbs per year.

Step-by-step explanation:

Given information: Estelle weight is

At age 16 = 110 lbs

At age 21 = 128 ibs

Increase in her weight over the past 5 years is the difference of weight at age 21 and at age 16.

Increase in her weight over the past 5 years = 128 - 110 = 18

Her weight is increase by 18 lbs over past five years.

Let x=age and y=weight, then the weight function passes through the points (16,110) and (21,128).

If a line passes through two points $(x_1,y_1)$ and $(x_2,y_2)$ , then the slope of the line is

$m=\frac{y_2-y_1}{x_2-x_1}$

Using the above formula we get

$m=\frac{128-110}{21-16}$

$m=\frac{18}{5}$

$m=3.6$

Therefore the slope is 3.6 lbs per year.

7 0

3 years ago

Identify each sequence as arithmetic or geometric. Explain your answer, and write an explicit formula for the

hammer [34]

Answer:

Arithmetic sequence

$a_n=\frac{1}{2}-n$ for $n\geq 1$

Step-by-step explanation:

We are given that a sequence

$-\frac{1}{2},-\frac{3}{2},-\frac{5}{2},-\frac{7}{2},...$

We have to identify the sequence as arithmetic or geometric and write an explicit formula .

$a_1=-\frac{1}{2}$

$a_2=-\frac{3}{2}$

$a_3=-\frac{5}{2}$

$a_4=-\frac{7}{2}$

$d_1=a_2-a_1=\frac{-3}{2}+\frac{1}{2}=-1$

$d_2=a_3-a_2=-\frac{5}{2}+\frac{3}{2}=-1$

$d_1=d_2=-1$

When the difference of consecutive terms is constant then the sequence is an arithmetic.

Hence, the sequence is an arithmetic.

$a_n=a+(n-1)d$

$a_n=-\frac{1}{2}+(n-1)(-1)=-\frac{1}{2}-n+1=\frac{1}{2}-n$ for $n\geq 1$

3 0

3 years ago

Chelsea is covering the outside of an old toy box with decorative paper. The box measures 6 inches by 14 inches by 3 inches.

olga nikolaevna [1]

Answer:

She will be needing 300 square inches of paper

length=14inches

breadth=3inches

height=6inches

TSA= 2(lb+lh+bh)

=2(14×3+14×6+3×6)

=2(42+84+24)

=2×150

=300 square inches

5 0

3 years ago

Need to be show how to solve step by step. And find a least common multiple

Firlakuza [10]

A cheap way to go about it is, use the LCD and multiply both sides by it.

now, notice the denominators, x, 4, 4x, clearly the LCD is 4x, so let's multiply both sides by that, to do away with the denominators,

$\bf \cfrac{5}{x}+\cfrac{3}{4}=\cfrac{8}{4x}\implies \boxed{4x}\left( \cfrac{5}{x}+\cfrac{3}{4} \right)=\boxed{4x}\cdot \cfrac{8}{4x}\implies 20+3x=8
\\\\\\
3x=-12\implies x=\cfrac{-12}{3}\implies x=-4$

8 0

3 years ago