Mathematics: How many 1/5 cup servings are in 3/4 of a cup of ice cream

How many 1/5 cup servings are in 3/4 of a cup of

cynthiakk

21.11.2020

The equation of the line that is parallel to the given line is:

y = 4x+12

Step-by-step explanation:

We know that the slope-intercept form of the line equation is

y=mx+b

where m is the slope and b is the y-intercept

Given the points of the gradient line

(0, -1)(3, 1)

Finding the slope between to points of the line

$\mathrm{Slope}=\frac{y_2-y_1}{x_2-x_1}$

$\left(x_1,\:y_1\right)=\left(0,\:-1\right),\:\left(x_2,\:y_2\right)=\left(3,\:1\right)$

$m=\frac{1-\left(-1\right)}{3-0}$

$m=\frac{2}{3}$

Thus, the slope of the gradient line = m = 2/3

We know that parallel lines have equal slopes. i.e. m₁ = m₂

Thus, the slope of the line parallel to the given line = m₂ = 4

Since the new line has an x-intercept of –3.

i.e. (x₁, y₁) = (-3, 0)

Thus, substituting m = 4 and the point (-3, 0) in the point-slope form of the equation line

$y-y_1=m\left(x-x_1\right)$

substituting the values m = 4 and the point (-3, 0)

y - 0 = 4(x-(-3))

$y=4\left(x+3\right)$

y = 4x+12

Therefore, the equation of the line that is parallel to the given line is:

y = 4x+12

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