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2 years ago

Find an equation in slope-intercept form for the line with slope -3/4 and y-intercept = 0

Mathematics

2 answers:

Lorico [155]2 years ago

4 0

Slope-intercept form: y = mx + b

The equation in <em>slope-intercept form</em> is y = -3/4x + 0 or y = -3/4x

<em>Hope this helps! :) -from peachimin</em>

love history [14]2 years ago

3 0

The slope intercept form:

y = mx + b

m - slope

b - y-intercept

We have: $m=-\dfrac{3}{4},\ b=0$

Therefore we have the equation:

$y=-\dfrac{3}{4}x+0\to\boxed{y=-\dfrac{3}{4}x}$

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Suppose a and b are the solutions to the quadratic equation 2x^2-3x-6=0. Find the value of (a+2)(b+2).

KonstantinChe [14]

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(a+2)(b+2) = 4

Step-by-step explanation:

We are given the following quadratic equation:

$2x^2-3x-6=0$

Let a a and b be the solution of the given quadratic equation.

Solving the equation:

$2x^2-3x-6=0\\\text{Using the quadratic formula}\\\\x = \dfrac{-b \pm \sqrt{b^2-4ac}}{2a}\\\\\text{Comparing the equation to }ax^2 + bx + c = 0\\\text{We have}\\a = 2\\b = -3\\c = -6\\x = \dfrac{3\pm \sqrt{9-4(2)(-6)}}{4} = \dfrac{3\pm \sqrt{57}}{4}\\\\a = \dfrac{3+\sqrt{57}}{4}, b = \dfrac{3-\sqrt{57}}{4}$

We have to find the value of (a+2)(b+2).

Putting the values:

$(a+2)(b+2)\\\\=\bigg(\dfrac{3+\sqrt{57}}{4}+2\bigg)\bigg(\dfrac{3-\sqrt{57}}{4}+2\bigg)\\\\=\bigg(\dfrac{11+\sqrt{57}}{4}\bigg)\bigg(\dfrac{11-\sqrt{57}}{4}\bigg)\\\\=\dfrac{121-57}{156} = \dfrac{64}{16} = 4$