Question

a line passes through the points (4, 19) and (9, 24). Write a linear function in the form y= mx + b for this line

Answer 1

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':

$\frac{24 - 19}{9 - 4}=\frac{5}{5}$=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.