Find a formula for a linear function that has x-intercepts 14 and y- intercept -16?

Question

Find a formula for a linear function that has x-intercepts 14 and y- intercept -16?

Answer 1

I would simply use the slope formula

(y2 - y1) / (x2 - x1) = m

(-16 -0) / (0 - 14) = (-16)/(-14) = 8/7

Then, using either the point-slope equation

y - y1 = m(x - x1)

or the slope-intercept equation

y = mx + b

with either point, you can verify that b=-16.

It's a good check on what you already know.

Answer 2

To find the equation for a linear function with specific x-intercepts and y-intercept, we use the formula for a line: y = mx + b, where m is the slope and b is the y-intercept.

1. Y-intercept: The y-intercept is -16, so b = -16.
2. X-intercepts: The x-intercepts are the points where the line crosses the x-axis, which makes y = 0. The given x-intercepts are x = 14.

We start by finding the slope m using one of the x-intercepts and the y-intercept:

The formula for the point-slope form of a line is y - y1 = m(x - x1).

Using y1 = -16 and x1 = 14, we get:

0 - (-16) = m(14 - 0)

16 = 14m

m = 16 / 14

m = 8 / 7

Now we can write the equation of the line using the slope m and the y-intercept b:

y = 8/7x - 16

This gives us the equation for the linear function with x-intercepts at 14 and y-intercept at -16.