Question

I forgot how to find the slope and y-intercept of the equation. For example y=3/4x - 5

Answer 1

The slope of any equation of the curve is defined as the rate of change in y-coordinate with respect to rate of change in x- coordinate

`\text{Slope}=\frac{y_2-y_1}{x_2-x_1_{}_{}}`
`\text{Slope}=(dy)/(dx)\text{ }`

Differentiate the given equation with respect to x

`\begin{gathered} y=(3)/(4)x-5 \\ \frac{dy\text{ }}{dx}=(3)/(4)-0 \end{gathered}`

Thus, the slope of the equation is 3/4

or Slope of the equation y=3/4x-5 is 3/4.

Now, for the y-intercept

Put x=0 in the equation

`\begin{gathered} y=(3)/(4)x-5 \\ y=(3)/(4)(0)-5 \\ y=-5 \end{gathered}`

The y-intercept of the equation y=3/4x-5 is y=(-5)