Question

A line passes through (4, 5) and (8, 9). Which equation best represents the line?

Answer 1

Find the slope of the line that will go through point (4, 5) and (8, 9) first and then you can use the point-slope form to figure out the equation of the line. Since I am not sure what form of the equation they want, I will just provide you the point-slope form, standard form, and the slope-intercept form of the line. 

The slope can be calculated by subtracting the difference of the y-coordinates of the two points and then dividing it by the difference of the x-coordinates. 

(y_2 - y_1) / (x_2 - x_1) = slope
(9 - 5) / (8 - 4) = 4 / 4 = 1

The point-slope form is: y - y_1 = m(x - x_1)
Let's take the coordinate (4, 5) and use 4 for x_1 and 5 for y_1. 
y - 5 = 1(x - 4) 

The slope-intercept form is: y = mx + b
We can modify the point-slope form to look like the slope-intercept form. 
y - 5 = 1(x - 4) 
y = x - 4 + 5
y = x + 1

The standard form is: ax + by = c
We can modify the slope-intercept form to look like the standard form.
y = x + 1
y - x = 1
-x + y = 1

Point-slope form: y - 5 = 1(x - 4) 
Slope-intercept form: y = x + 1
Standard form: -x + y = 1