Answered

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D. Rearrange the equation to solve for the slope, m. Is this equivalent to the equation for slope given inquestion 4F above? Explain,

D Rearrange The Equation To Solve For The Slope M Is This Equivalent To The Equation For Slope Given Inquestion 4F Above Explain class=

Sagot :

If we say

[tex]y-y_1=m(x-x_1)[/tex]

then dividing both sides by (x - x_1) gives

[tex]\frac{1}{x-x_1}\times(y-y_1)=m(x-x_1)\times\frac{1}{x-x_1}[/tex]

[tex]\therefore m=\frac{y-y_1}{x-x_1}[/tex]

which is our answer!

The above equation correctly gives the slope m because it is in accord with the definition of m as rise / run.

(E).

Let us now expand the RHS of the first equation to get:

[tex]y-y_1=mx-mx_1[/tex]

Adding y_1 to both sides gives

[tex]\textcolor{#FF7968}{y=mx-mx_1+y_{1.}}[/tex]

Or in a more neat form

[tex]\textcolor{#FF7968}{y=mx+(y_1-mx_1)}\text{\textcolor{#FF7968}{.}}[/tex]

(F).

As can be seen from the equation y = mx + b we got in E, the y-intercept b is given by

[tex]\textcolor{#FF7968}{b=y_1-mx_{1.}}[/tex]

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