How do you write the point slope form of the equation given (-3,4) and (0,3)?

Answer 1

#y-3=-1/3(x-0)#

The equation of a line in #color(blue)"point-slope form"# is.
#color(red)(bar(ul(|color(white)(a/a)color(black)(y-y_1=m(x-x_1))color(white)(a/a)|)))# where m represents the slope and # (x_1,y_1)# a point on the line.
To calculate the slope use the #color(blue)"gradient formula"#
#color(red)(bar(ul(|color(white)(a/a)color(black)(m=(y_2-y_1)/(x_2-x_1))color(white)(a/a)|)))# where # (x_1,y_1)" and " (x_2,y_2)" are 2 coordinate points".#

here the 2 points are (-3 ,4) and (0 ,3)

let # (x_1,y_1)=(-3,4)" and " (x_2,y_2)=(0,3)#
#rArrm=(3-4)/(0+3)=-1/3#
Using either of the 2 given points for #x_1,y_1)#
Using (0 ,3) and m# =-1/3# substitute these values into the point-slope equation.
#y-3=-1/3(x-0)larr" point-slope form"#

If we distribute the brackets and rearrange .

or #y=-1/3x+3larr" slope-intercept form"#
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Answer 2

To write the point-slope form of the equation given two points ((-3, 4)) and ((0, 3)), follow these steps:

  1. Calculate the slope ((m)) using the formula: [m = \frac{y_2 - y_1}{x_2 - x_1}]

  2. Substitute the coordinates ((x_1, y_1)) and ((x_2, y_2)) into the formula: [m = \frac{3 - 4}{0 - (-3)}] [m = \frac{-1}{3}]

  3. Choose one of the points, let's say ((-3, 4)), and substitute the slope ((-1/3)) into the point-slope form: [y - y_1 = m(x - x_1)] [y - 4 = -\frac{1}{3}(x - (-3))] [y - 4 = -\frac{1}{3}(x + 3)]

So, the point-slope form of the equation is: [y - 4 = -\frac{1}{3}(x + 3)]

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Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

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