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Use the coordinates of the labeled point to find the point-slope equation of the line

Use The Coordinates Of The Labeled Point To Find The Pointslope Equation Of The Line class=

Sagot :

Answer:

[tex]y + 5 = -4(x - 2)[/tex], option b.

Step-by-step explanation:

Equation of a line:

The equation of a line, in point-slope form, is given by:

[tex]y - y_0 = m(x - x_0)[/tex]

In which m is the slope and [tex](x_0,y_0)[/tex] is the point.

Point (2,-5)

This means that [tex]x_0 = 2, y_0 = -5[/tex]. So

[tex]y - y_0 = m(x - x_0)[/tex]

[tex]y - (-5) = m(x - 2)[/tex]

[tex]y + 5 = m(x - 2)[/tex]

Finding the slope:

When we have two points, the slope is given by the change in x divided by the change in y.

In this question, we have points (0,3) and (2,-5). So

Change in y: 3 - (-5) = 3 + 5 = 8

Change in x: 0 - 2 = -2

So

[tex]m = \frac{8}{-2} = -4[/tex]

Then, the equation of the line is:

[tex]y + 5 = -4(x - 2)[/tex], option b.

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