Answer:
y = x + 15
Step-by-step explanation:
Linear functions are typically written in slope-intercept form, y = mx + b, where 'm' is equal to the slope of the line and 'b' is equal to the y-intercept. When given two points on the line, the first step is to identify the 'x' and 'y' corrodinates (4, 19) x = 4, y = 19 and (9, 24) x = 9 and y = 24. Slope is a fraction of the change in 'y' over the change in 'x':
[tex]\frac{24 - 19}{9 - 4}=\frac{5}{5}[/tex]=1
So, the slope, or 'm' is equal to 1. The next step is to solve for 'b', or the y-intercept. You can use the slope-intercept formula and use the slope and one of the given points to solve for 'b':
y = mx + b or 19 = (1)(4) + b or 19 = 4 + b, subtract 4 from both sides: 19 - 4 = 4 - 4 + b. This leaves b = 15.
Plugging in our values for 'm' (1) and 'b' (15): y = x + 15.
