Mathematics, 29.01.2020 06:48 kayla114035

What is the y-coordinate fo the y-intercept of the line that passes through the points (-4,-4) and (4,8)

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Answer from: amara71

y = 2

Step-by-step explanation:

Because we need to find the y-intercept, we should find the equation of the line in slope-intercept form (y = mx + b).

"x" and "y" represent a point on the line.

"m" represents the slope (how steep the line is).

"b" represents the y-intercept (where the line hits the y-axis).

Given the two coordinates on the line, use the formula to find slope: $m = \frac{y_{2}-y_{1}}{x_{2}-x_{1}}$

Choose which point will be point 1 and point 2. Remember points are written (x, y).

Point 1 (-4, -4) x₁ = -4 y₁ = -4

Point 2 (4, 8) x₂ = 4 y₂ = 8

Substitute the information from the coordinates into the slope formula.

$m = \frac{y_{2}-y_{1}}{x_{2}-x_{1}}$

$m = \frac{8-(-4)}{4-(-4)}$ Simplify the numerator and denominator

$m = \frac{12}{8}$ Reduce the fraction. Top and bottom can divide by 4.

$m = \frac{3}{2}$ Slope of the line, m = 3/2

Since we know at least one point on the line and the slope, we only have one missing piece of information in the equation y = mx + b.

Substitute a random point (4,8) and the slope (3/2) into the equation. Then isolate "b" to find the y-intercept.

y = mx + b

$8 = (\frac{3}{2})(4) + b$ Multiply 3/2 and 4 by combining into the numerator

$8 = \frac{3*4}{2} + b$ Simplify the fraction. 12/2 = 6

8 = 6 + b Isolate "b"

8 - 6 = b Subtract 6 from both sides

b = 2 Write variable on left side for standard formatting.

Therefore the y-coordinate for the y-intercept of the line is 2.

Answer from: Quest

In all honesty, there really is no “work” per say to show. mainly it’s just using the process of elimination. the question is asking which domain(s) would be the most appropriate for the function c(n). n is the number of observed vehicles so right away, 1, 2, and 3 can be eliminated.why? 1, 2 start in the negatives and therefore it is impossible to observe negative cars. so, #4 would be the best answer to the given problem.

Answer from: Quest

answer is 8x+24

area of vanessa's patio = length × width

given, length = (3x² + 5x + 10)

width = (x² - 3x - 1)

area of vanessa's patio = (3x² + 5x + 10)(x² - 3x - 1)

= 3x²(x² - 3x - 1) + 5x(x² - 3x - 1) + 10(x² - 3x - 1)

= 3x⁴ - 9x³ - 3x² + 5x³ - 15x² - 5x + 10x² - 30x - 10

= 3x⁴ - 4x³ - 8x² - 35x - 10

hence, expression of vanessa's patio = (3x⁴ - 4x³ - 8x² - 35x - 10)

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