$\text{The slope of the line t:}\ m=-\dfrac{3}{4}\\\\\text{The y-intercept of the line t:}\ b=2\\\\\text{The equation of a line t in the slope-intercept form:}\ y=-\dfrac{3}{4}x+2$

Step-by-step explanation:

The slope-intercept form of an equation of a line:

$y=mx+b$

m - slope

b - y-intercept → (0, b)

The formula of a slope:

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

We have two points (8, -4) and (0, 2) → b = 2.

Calculate the slope:

$m=\dfrac{2-(-4)}{0-8}=\dfrac{6}{-8}=-\dfrac{3}{4}$

Therefore the equation of a line t in the slope-intercept form is:

$y=-\dfrac{3}{4}x+2$

5 0

3 years ago

Read 2 more answers

A manufacturer compares its income f(x) to its expenses g(x) for x number of units sold. What does the solution to f(x) = g(x) r

Aliun [14]

Answer: The number of units sold when the manufactures home income equals the manufactures expenses

Step-by-step explanation:

3 0

3 years ago

Calculate the average rate of change for the function f(x)=x^4+3x^3-5x^2-2, from x=-1 to x=1

PSYCHO15rus [73]

∫ f(x) dx = x⁵/5 + 3x⁴/4 - 5x³/3

-1

[1⁵/5 + 3⁴/4 - 5³/3] - [ -1⁵/5 -3⁴/4 +5³/3]

plug that into your calculator and that's your rate of change

5 0

3 years ago

The triangles below are similar. By what ratio was triangle XYZ enlarged by to create triangle LMN? Use this information to calc

aliina [53]

Answer:

Ratio: 3:2

LN = 18

Step-by-step explanation:

"similar" means that all the angles are the same and the sides were all increased by the same proportion.

Thus, we know that MN/YZ = LM/XY = NL/ZX

First, we need to find the ratio. To do this, we write MN/YZ as a fraction, and simplify.

MN/YZ = 15/10 = 3/2

(If you want, you can double check this using LM nd XY. 8 * 3/2 = 12, so this is correct)

To find the missing side, we simply multiply XZ by 3/2.

12 * 3/2 = 18, so LN = 18.

4 0

3 years ago