How do you write an equation of a line given point (3,3) and m=4/3?

Answer 1

See the solution process below:

The point-slope formula states: #(y - color(red)(y_1)) = color(blue)(m)(x - color(red)(x_1))#
Where #color(blue)(m)# is the slope and #color(red)(((x_1, y_1)))# is a point the line passes through.

Substituting the slope and values from the points in the problem gives:

#(y - color(red)(3)) = color(blue)(4/3)(x - color(red)(3))#
We can solve for #y# to transform the equation to the slope-intercept form.The slope-intercept form of a linear equation is: #y = color(red)(m)x + color(blue)(b)#
Where #color(red)(m)# is the slope and #color(blue)(b)# is the y-intercept value.
#y - color(red)(3) = (color(blue)(4/3) * x) - (color(blue)(4/3) * color(red)(3))#
#y - color(red)(3) = 4/3x - 4#
#y - color(red)(3) + 3 = 4/3x - 4 + 3#
#y - 0 = 4/3x - 1#
#y = color(red)(4/3)x - color(blue)(1)#
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Answer 2

The equation of a line given a point (x1, y1) and slope m is: ( y - y_1 = m(x - x_1) ). Substituting (3,3) and m = 4/3, the equation becomes: ( y - 3 = \frac{4}{3}(x - 3) ). Simplify it to: ( y - 3 = \frac{4}{3}x - 4 ). Then, solve for y to get the final equation: ( y = \frac{4}{3}x - 1 ).

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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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