Question

How do you find the slope and intercept of $2x + 5y = 10$?

Answer 1

We know the equation of a line passing through a point and having a slope ‘m’ and with ‘y’ intercept as ‘b’ is given by $y = mx + b$. Here (x, y) is a variable. We convert the given equation to the slope intercept form. Then comparing the simplified equation with the equation of slope intercept we will get the desired result.

Complete step by step solution:
Given, $2x + 5y = 10$.

As we can see that we have a slope intercept equation $y = mx + b$. We need to solve the given
equation for ‘y’.

Subtracting ‘2x’ on both sides of the equation,
$\Rightarrow 5y = 10 - 2x$

Divided the whole equation by 5 we get:
$\Rightarrow \dfrac{{5y}}{5} = \dfrac{{10 - 2x}}{5}$

Dividing and separating the terms in the right hand side of the equation,
$\Rightarrow y = \dfrac{{10}}{5} - \dfrac{{2x}}{5}$

Rearranging we have,
$\Rightarrow y = - \dfrac{{2x}}{5} + \dfrac{{10}}{5}$

Again dividing we get,
$\Rightarrow y = - \dfrac{{2x}}{5} + 2$

Thus we have simplified the form of the given equation. Now comparing the equation $y = - \dfrac{{2x}}{5} + 2$ with the equation of slope intercept form $y = mx + b$. We can see that $m = \- \dfrac{2}{5}$ and ‘y’ intercept is 2.

That is we have $slope = - \dfrac{2}{5}$ and $y - {\text{intercept}} = 2$.

Note: ‘y’ intercept is defined as a line or a curve crosses the y-axis of a graph. In other words the value of ‘y’ at ‘x’ is equal to zero. Let’s put value of ‘x’ is equal to zero then, $2(0) + 5y = 10$ $\Rightarrow 5y = 10$ (Divide by 5 on both sides )
$\Rightarrow y = \dfrac{{10}}{5}$
$\Rightarrow y = 2$.
Thus we can see that we got the same y-intercept value. Here the slope is negative value, meaning that as the line on the line graph moves from left to right, the line falls.