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What is the equation of the line passing through #(18,2) # with slope #m= -4/7#?

Answer 1

Hazel Anglin

#y=-4/7x+12 2/7#

Slope-intercept form of an equation: #y=mx+b# where #m# is the slope and #b# is the y-intercept

#y=-4/7x+b rarr# The slope is given to us, but we do not know the y-intercept

Let's plug in the point #(18, 2)# and solve:

#2=-4/7*18+b#

#2=-72/7+b#

#2=-10 2/7+b#

#b=12 2/7#

#y=-4/7x+12 2/7#

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Answer 2

Eva Abramson

To find the equation of a line given a point ((x_1, y_1)) and the slope (m), you can use the point-slope form of the equation:

[ y - y_1 = m(x - x_1) ]

Using the point ((18, 2)) and the slope (m = -\frac{4}{7}):

[ y - 2 = -\frac{4}{7}(x - 18) ]

Now, you can distribute (-\frac{4}{7}) and then solve for (y) to get the equation in slope-intercept form (y = mx + b):

[ y - 2 = -\frac{4}{7}x + \frac{72}{7} ]

[ y = -\frac{4}{7}x + \frac{72}{7} + 2 ]

[ y = -\frac{4}{7}x + \frac{72}{7} + \frac{14}{7} ]

[ y = -\frac{4}{7}x + \frac{86}{7} ]

Therefore, the equation of the line passing through ((18, 2)) with slope (m = -\frac{4}{7}) is (y = -\frac{4}{7}x + \frac{86}{7}).

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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.