How to find the x-intercept from a table?

Question

If I have the table,

 

x         y
-5       -7
0        -5
5        -3

How would I find the x-intercept of this table?

Answer 1

What is an x-intercept? It's where the function or relation crosses the x-axis.

 

When that happens, what is y equal to?

 

When crossing the x-axis, y = 0.

 

There may be more information in your question, such as if this is a linear function. From the table, it appears to be a linear function because the change in x in relation to the change in y is constant. This is the slope.

Slope = change in y/change in x

Slope = (-7 - -5)/(-5 - 0) = (-7 + 5)/(-5) = -2/-5 = 2/5

 

If you have the slope, you can find an equation of the line using point-slope form:

(y₁ - y₂) = m (x₁ - x₂) 

where m = slope and (x₁, y₁) and (x₂, y₂) are points on the line. Leave y₁ and x₁ as just y and x for an equation and replace the second y and x with a point from your table, giving:

y - - 5 = 2/5 (x - 0)      I chose the point (0, -5) because the 0 for x makes it easy to plug in to the formula.

y + 5 = 2/5 x

 

Remember that the x-intercept happens when y = 0. What can you do now? Simple! Plug y = 0 into the formula!

 

0 + 5 = 2/5 x     Simplify.

5 = 2/5 x           Multiply by 5/2 to make the fraction = 1 so x is alone.

5 (5/2) = x         To multiply a fraction by a whole number, multiply the numerator by the whole number. 

25/2 = x            What is 25/2? Half of 24 is 12, and half of 1 is 0.5, so half of 25 (which is 24 + 1) is 12 + 0.5:

12.5 = x