Question

Drag equations to each row to show why the equation of a straight line is y = mx + b, where m is the slope and b is the y-intercept.

Answer 1

The equations will be y-b/ x =m/1, y-b=m(x) and y=mx +b

Step-by-step explanation:

In the diagram you can show the two triangles are similar by showing that the ratio of rise to rum is equal.This is  

y-b/ x =m/1  Multiplying both sides by x  y-b=m(x)  Adding b on both sides will eliminate the b on the left side as;  y-b+b= mx+b  y=mx +b where m is the slope and b is the y-intercept

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 To write the slope-intercept equation : https://brainly.com/question/10676927  

The slope intercept equation : https://brainly.com/question/11514369  

Keywords : slope intercept equation  

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Answer 2

Answer:

1. $\dfrac{y-b}{x}=\dfrac{m}{1}$     (The two triangles on the graph are similar).

2. $y-b=mx$         (Multiply both sides by x)

3. $y=mx+b$         (Add b on both sides)

Step-by-step explanation:

In the given graph two triangles are similar and corresponding parts of similar triangles are proportional.

$\dfrac{y-b}{x}=\dfrac{m}{1}$     (The two triangles on the graph are similar)

Multiply both sides by x.

$\dfrac{y-b}{x}\times x=\dfrac{m}{1}\times x$

$y-b=mx$

Add b on both sides.

$y-b+b=mx+b$

$y=mx+b$

Therefore, y=mx+b is a slope intercept form of a straight line, where m is the slope and b is y-intercept.