Mathematics, 03.02.2020 23:52 tsmittens137

What is an equation of the line that is perpendicular to y=-4/5x +3 and passed through the point (4,12)

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Answer from: rodres17

$\large\boxed{y=\dfrac{5}{4}x+7}$

Step-by-step explanation:

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

y=mx+b

m - slope

b - y-intercept

We have

$y=-\dfrac{4}{5}x+3\to m_1=-\dfrac{4}{5}$

If k:y=m_1x+b_1 and l:y=m_2x+b_2 , then

$l\ \perp\ k\iff m_1m_2=-1\to m_2=-\dfrac{1}{m_1}$

Calculate the slope:

$m_2=-\dfrac{1}{-\frac{4}{5}}=\dfrac{5}{4}$

Therefore e have the equation of a line:

$y=\dfrac{5}{4}x+b$

The line passes through the point (4, 12). Put the coordinates of the point to the equation of a line:

$12=\dfrac{5}{4}(4)+b$

12=5+b subtract 5 from both sides

$7=b\to b=7$

Finally:

$y=\dfrac{5}{4}x+7$

Answer from: Quest

the solution is h=10 because you add 9 to each side of the equation.

Answer from: Quest

ratios represent a pattern or relationship that can be scaled.

equivalent ratios are pairs of ratios that represent the same relationship between quantities, and can be generated by multiplying or dividing both quantities in the ratio by the same factor.

in this lesson, students will use double number lines and ratio reasoning to solve ratio problems. by partitioning double number lines into proportionate intervals, students will build an understanding of equivalent ratio relationships as those that are generated by multiplying or dividing two related quantities by the same number. this lesson will build upon students' prior understanding of multiplicative comparisons, number line reasoning and equivalent fractions (while highlighting the difference between equivalent fractions and equivalent ratios); and will build toward future work in this unit on building ratio tables, and work in future grades in proportionality, scaling, and expressing and graphing linear functions.

step-by-step explanation:

ratios represent a pattern or relationship that can be scaled.

equivalent ratios are pairs of ratios that represent the same relationship between quantities, and can be generated by multiplying or dividing both quantities in the ratio by the same factor.

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