using point 1, P1 (6,4) and slope m =4/3, substitutes these values in Equation 1

Formula memory recall: y = mx + b in slope form --equation 1

Using Point 1 (x=6, y=4) y1 = 4 substitute y = 4 in equation 1 ; then x1 = 6
Finally m = 1.33
Why ? In order to get the original value of b at point 1 coordinate (6,4)
After you input the value of y1, x1, and slope, m. It should look like shown below.

y₁ = m * x₁ + b

To do scenario analysis, simply change any value in white input box. Answer is automatic.

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b = is the answer for variable "b" after doing algebraic calculation from above equation 1.

Using the value of b, we can discover the general pattern of this line equation which is
y = 1.33x - 3.98. This line equation is the description of the general behavior of any points along the line. What it means is with this line equation we can predict or solve any position of a point in "y" axis if we are given any position of "x" axis.

So let's use this discovered pattern of line equation to predict the value of new "y" when the given value of x = 0 .

Mathematical expression such as P2(0, y) seems to be of no meaning if you are not taught by a mathematician who knows how to interpret its meaning. It means the author of this math expression is telling you to predict or solve the value of y in y-axis using the value of x = 0.

You can't solve P2(0,y) if you don't discover the line equation from the given problem. But the author of this problem wants you to do more after you solve the value "y" when x = 0. The author wants you to find the distance between the two points.

To find the distance between two points, you need to memory recall your acquired knowledge about Pythagorean equation formula and relate it to slope formula and right triangle formula. Finally c² = a² + b² or c = √ 6² + 8²

a = (6-0) = 6 ; X₁ b = (4-(-3.98)) ~ 8 . Answer = √100 = 10 Learning mathematics is a very good brain exercise to connect your previous acquired memories in your brain neuron.

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The discovered line equation will be shown below

y = x + written in slope form.

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using point, P2 ( y₂) substitutes its values in equation of a line.

To do scenario analysis, simply change the value in any white input box. Answer is automatic.

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y₂ = * + written in slope form.

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y₂ =

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Given
P1 ( x₁ , y₁ )

Given
P2 ( x₂ , y₂ )

Distance, d =

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