in this lesson you will learn how to find the slope and why intercept of a line from any linear equation we will cover examples in slope intercept form standard form as well as equations with no xterm or Y term in slope intercept form the coefficient of x represents the slope of the line the Y intercept is the point 0 comma B it is where the line crosses the y- axis and at this point the x coordinate is always zero our first example is in slope intercept form the coefficient of x is 6 so the slope is 6 B is 1 so the Y intercept is 0a 1 this is where the line crosses the Y AIS what if there is no number in front of X that means the coefficient is one so the slope is one remember min-2 is the same as + -2 so B is -2 and the Y intercept is 0 comma -2 what if there is only a negative sign in front of X that means the coefficient is -1 so the slope is neg 1 B is -7 so the Y intercept is 0a -7 notice that when you rewrite the equation to look like y = mx + b it becomes much easier to recognize both the slope and the Y intercept now try this one what are the slope and Y intercept you can re write this as y = -3x + 5 this is the same as our original equation but it looks like this right so now it is clear that the slope is -3 and the Y intercept is 0a 5 what if there is no constant term what does that mean for the Y intercept no constant term means b equals 0 so the slope is 2 over 3 and the Y intercept is 0a 0 now let's take a look at a new kind of equations this equation has no X term at all what does that mean for the slope Y = 2 means the value of y is always 2 no matter the value of x if you graph it you will see that it is a horizontal line crossing the y- axis at two the slope of any horizontal line is zero because there is no vertical change so the slope here is 0er since the line crosses the y- AIS at 2 the Y intercept is 0 comma 2 in general if an equation is in the form y equals K where K is a constant then the slope is zero and the Y intercept is 0a K now let's flip the scenario what happens if there is no y term in the equation x = -3 means the value of x is always -3 no matter the value of y if you graph it you will see it is a vertical line crossing the x-axis at -3 the slope of any vertical line is defined because there is no horizontal change so the slope here is undefined since the line doesn't cross the y- AIS it has no Y intercept in general if an equation is in the form xal K where K is a constant then the slope is undefined and there is no Y intercept for more on the slope of vertical and horizontal lines using rise and run check the link in the description now what if the equation is in standard form first convert the standard form to slope intercept form by isolating y on one side of the equation start by subtracting the X term from both sides on the left side these cancel out leaving 2 y on the right side we get -5x + 6 we write the X term first because in slope intercept form the X term comes first on the right side of the equation then divide both sides by two to isolate y remember to divide every term these cancel out leaving y by itself 6 / 2 is three right now our equation is in slope intercept form so the slope is -5 / 2 B is 3 so the Y intercept is 0a 3 we are almost done pause the video and try our last example first rewrite it in slope intercept form start by subtracting X from both sides then divide both sides by -4 these cancel out leaving y the negative signs cancel out leaving 1/4x -8 / -4 is 2 right now the equation is in slope intercept form and you can see that the slope is 1 over4 and the Y intercept is 0a 2 to learn how to graph a linear equation using the slope and Y intercept check the link in the description give it a thumbs up and consider subscribing