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The points (10, -8) and (9, t) fall on a line with a slope of 0. what is the value of t?

Answer 1

Abigail Allen

#t=-8#

gradient (slope) #=("change in up or down")/("change in along")" "#

as you move along the x-axis from left to right.

Gradient = 0 gives rise to:

#("change in up or down")/("change in along")" " = (y_2-y_1)/(x_2-x_1)=0/(x_2-x_1)#

If the gradient is 0 then the line is horizontal. Thus the value of #y# is constant #(y_2=y_1)#

Given that point 1 #" "P_1->(x_1,y_1)=(10,-8)#

Then the constant value of y is -8 ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ However, the question uses the letter #t# instead of #y# so #t# is a constant at #t=-8#

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Answer 2

Isaiah Anthony

The slope of a line is given by the formula: ( \text{slope} = \frac{{\text{change in y}}}{{\text{change in x}}} ). Given that the slope is 0 and the points are (10, -8) and (9, t), we can set up the equation ( \frac{{t - (-8)}}{{9 - 10}} = 0 ) and solve for t. Simplifying the equation yields ( \frac{{t + 8}}{{-1}} = 0 ). Solving for t, we find that ( t = -8 ).

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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.