# How do you find the slope and y intercept for y=3-5/4x?

Sep 17, 2015

$m = - \frac{5}{4}$
$B = 3$

#### Explanation:

The slope is the value that multiplies the variable. We know the formula $m = \frac{\Delta y}{\Delta x}$

By using the generic function $y = a x + b$ we can show that a is always the slope.

$m = \frac{{y}_{f} - {y}_{i}}{{x}_{f} - {x}_{i}}$
$m = \frac{a {x}_{f} + b - a {x}_{i} - b}{{x}_{f} - {x}_{i}}$
$m = \frac{a \left({x}_{f} - {x}_{i}\right) + b - b}{{x}_{f} - {x}_{i}}$
$m = a \cdot \frac{\cancel{{x}_{f} - {x}_{i}}}{\cancel{{x}_{f} - {x}_{i}}}$
$m = a$

So, when we apply it to this function, we see that $m = - \frac{5}{4}$

The y-intercept is simply the value of the function when $x = 0$, and is always the value without a variable. We can show it by using the generic function.

$B = a x + b$
$B = a \cdot 0 + b$
$B = b$

So, for this function, the y-intercept is 3.