# The equation y=2x-3 has what type of slope?

Mar 4, 2018

It is a straight line

#### Explanation:

In this type of equation, as it is written in the form $y = m x + c$. The graph is always a straight line. $y$ stands for the $y$ coordinate, $m$ stands for the gradient, and $c$ stands for the $y$ intercept.

We can check this by plugging in some values for $x$

$x = - 1$
$y = 2 \left(- 1\right) - 3 = - 5$

$x = 0$
$y = 2 \left(0\right) - 3 = - 3$

$x = 1$
$y = 2 \left(1\right) - 3$=-1

$x = 2$
$y = 2 \left(2\right) - 3 = 1$

$x = 3$
$y = 2 \left(3\right) - 3 = 3$

The $y$ intercept is always the $y$ value when $x = 0$, so, therefore, the $y$ intercept value $= - 3$. As shown in the equation.

As you can see, when the $x$ value is increased by one, the $y$ value increases by two, or when the $x$ value decreases by one, the $y$ value decreases by two. Since all the differences are the same, the graph should look like a straight line as pictured below.

Since $m$ is $> 0$, it is a positive slope, if there was no $m$, there would just be a straight line going across whatever the $y$ intercept was, in this case $- 3$

When drawing the graph written in the form $y = m x + c$, draw around five points, including some negative, positive, and $0$ like I have in the table above.

graph{y=2x-3 [-7.023, 7.024, -3.51, 3.513]}