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: $\frac{y_{2}-y_{1} }{x_{2}-x_{1}}$. 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: $\frac{16-6}{9-4} = \frac{10}{5} = 2$

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.