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: [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1}}[/tex]. We can assign the point (4, 6) to [tex]x_{1}[/tex] and [tex]y_{1}[/tex] and (9, 16) to [tex]x_{2}[/tex] and [tex]y_{2}[/tex].
Now, we can find the slope: [tex]\frac{16-6}{9-4} = \frac{10}{5} = 2[/tex]
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.
