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Wittaler [7]
2 years ago
11

A line passes through the points (0, 9) and (9, 19). What is its equation in slope-intercept form?

Mathematics
1 answer:
STatiana [176]2 years ago
3 0

Answer:

y = 10/9x + 9

Step-by-step explanation:

To write the equation in its slope-intercept form, y = mx + b, we need to find the slope (m) of the line and its y-intercept (b).

Given the points (0, 9) and (9, 19), we can solve for the slope of the line using the following formula:

m = \frac{y2 - y1}{x2 - x1}

Let (x1, y1) = (0, 9)

and (x2, y2) = (9, 19)

Substitute these values on the formula:

m = \frac{y2 - y1}{x2 - x1} = \frac{19 - 9}{9 - 0} = \frac{10}{9}

Therefore, the slope (<em>m </em>) = 10/9.

Next, the <u>y-intercept</u> is the point on the graph where it crosses the y-axis, and has the coordinates, (0, <em>b </em>). It is also the value of the y when x = 0.

One of the given points is the y-intercept of the line, given by (0, 9). The y-coordinate, 9, is the value of b.

Therefore, the linear equation in slope-intercept form is: y = 10/9x + 9

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A rectangular garden must have a perimeter of 150 feet and an area of at least 1200 square feet. Describe the possible lengths o
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Answer: 51.86 and 23.14

Step-by-step explanation:

The rectangular garden must have a perimeter of 150 feet

Perimeter of rectangular garden =

2l + 2w=150 -----------1

The rectangular garden must have a perimeter of 150 feet and an area of at least 1200 square feet.

Area of rectangular garden =

l×w= 1200 feet^2 -----------2

From equation 2, l=1200/w

Put l=1200/w in equation 1

2× 1200/w + 2w = 150

(2400/w) +2w = 150

(2400+2w^2)/w =150

2400+2w^2= 150w

2w^2- 150w+2400=0

Using the general formula

w = [-b+-√(b^2-4ac)]/2a

a = 2, b =-150, c=2400

w =[--150+/-√(-150^2-4×2×2400)]/2×2

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=[150+/-√3300)]/4

=(150+57.45)/4 or (150-57.45)/4

w= 207.45/4 or 92.55/4

w= 51.86 or w= 23.14

l = 1200/51.86 or l= 1200/23.14

l = 23.14. or l= 51.86

For an area of at least 1200ft^2

The dimensions are 51.86 and 23.14

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