Final answer:
The linear function that satisfies the given values f(0)=10 and f(6)=34 is f(x)=4x+10, where the slope is calculated as 4 and the y-intercept is 10.
Step-by-step explanation:
To write a linear function f(x) with the given values f(0) = 10 and f(6) = 34, we first need to find the slope of the line. The slope can be calculated using the formula (change in y)/(change in x), which would be (34-10)/(6-0) = 24/6 = 4.
So, the slope is 4.
Using the slope and one of the points,
we can write the equation in point-slope form: y - y1 = m(x - x1), where m is the slope and (x1, y1) is a point on the line.
Plugging in the slope and the point (0, 10): y - 10 = 4(x - 0).
Finally, to write it in slope-intercept form,
we solve for y: y = 4x + 10. This is the equation of the linear function that satisfies both given conditions.