Question

Which equation represents a line that passes through (4, left-parenthesis 4, StartFraction one-third EndFractin right-parenthesis.) and has a slope of StartFraction 3 Over 4 EndFraction.?
y – y minus StartFraction one-third EndFraction equals StartFraction 3 Over 4 EndFraction left-parenthesis x minus 4 right-parenthesis. = y minus StartFraction 3 Over 4 EndFraction equals StartFraction one-third EndFraction left-parenthesis x minus 4 right-parenthesis.(x – 4)
y – y minus StartFraction one-third EndFraction equals 4 left-parenthesis x minus StartFraction 3 Over 4 EndFraction right-parenthesis. = y minus StartFraction one-third EndFraction equals StartFraction 3 Over 4 EndFraction left-parenthesis x minus 4 right-parenthesis.(x – 4)
y – y minus StartFraction one-third EndFraction equals 4 left-parenthesis x minus StartFraction 3 Over 4 EndFraction right-parenthesis. = 4(x – )
y – 4 = y minus 4 equals StartFraction 3 Over 4 EndFraction left-parenthesis x minus StartFraction one-third EndFraction right-parenthesis.(x – )

Answer 1

The equation represents a line that passes through(4, 1/3) and has a slope of 3/4 option A; y - 1/3 = 3/4 ( x - 4).

What is the Point-slope form?

The equation of the straight line has its slope and given point.

If we have a non-vertical line that passes through any point(x1, y1) has gradient m. then general point (x, y) must satisfy the equation

y-y₁ = m(x-x₁)

Which is the required equation of a line in a point-slope form.

we know that            

The equation of the line into point-slope form is equal to                        

y-y₁ = m(x-x₁)

             

we have          

(x₁, y₁) = (4, 1/3)

m = 3/4

 

substitute the given values                

y-y₁ = m(x-x₁)

y - 1/3 = 3/4 ( x - 4)

therefore,

y minus StartFraction one-third EndFraction equals StartFraction 3 Over 4 EndFraction left-parenthesis x minus 4 right-parenthesis.(x – 4)

Thus, option A is correct.

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