Home > Algebra > Write an Equation Given the Slope and a Point

How do you write an equation of a line given point (4,-6) and m=1?

Answer 1

See a solution process below:

We can use the point-slope formula to find the equation of the line. 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 point in the problem gives:

#(y - color(red)(-6)) = color(blue)(1)(x - color(red)(4))#

#(y + color(red)(6)) = color(blue)(1)(x - color(red)(4))#

If necessary, we can convert this equation to slope-intercept by solving for #y#. 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)(6) = x - color(red)(4)#

#y + color(red)(6) - 6 = x - color(red)(4) - 6#

#y + 0 = x - 10#

#y = color(red)(1)x - color(blue)(10)#

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Answer 2

Julia Adams

The equation of the line with slope m = 1 passing through the point (4, -6) is y = x - 10.

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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.