Question

Find the equation of the line in slope-intercept form containing the points (4,6) and (9,16).

Answer 1

Hello!

Slope-intercept form is y = mx + b. In this form, m is the slope and y is the y-intercept.

To find the slope, we need to use the slope formula. The slope formula is:
`(y_(2)-y_(1) )/(x_(2)-x_(1))`. We can assign the point (4, 6) to
`x_(1)` and
`y_(1)` and (9, 16) to
`x_(2)` and
`y_(2)`.

Now, we can find the slope:
`(16-6)/(9-4) = (10)/(5) = 2`

Next, we can find the y-intercept by substituting a point into the slope-intercept form with the slope as 2.

y = 2x + b (substitute a given point)

6 = 2(4) + b (simplify)

6 = 8 + b (subtract 8 from both sides)

-2 = b

Therefore, the equation of the line is y = 2x - 2.