4.1 exit ticket

Question

Write the equation of the line in slope intercept form given that f(0)=9 and f(1)=6

Answer 1

Hi Loni!

An equation of a line written in slope intercept form looks like y = mx + b, where m = slope and b = y intercept.

From what we are given, we know that when x = 0, y = 9. And when x = 1, y = 6. We can use this information to find the slope using the equation (y2 - y1)/(x2 - x1) = m, where x1 and x2 are the two x values, and y1 and y2 are the two y values. We can assign x1 = 0, y1 = 9, x2 = 1, and y2 = 6.

Plugging in our values gives us (6-9)/(1-0) = (-3)/(1) = -3. So the slope of the line, m = -3. Next, we can use point slope form to help us write the equation: y - y1 = m(x - x1).

When we plug in our values, we get y - 9 = -3(x - 0), which cleans up to:

y - 9 = -3x + 0, and then we add 9 to both sides so that we get the equation into slope intercept form.

y = -3x +9

Hope this helps!