Identifying Slope from Equation

Let's have a quick recap of what we know about straight lines on the Cartesian plane so far.

• They have a gradient (slope), a measure of how steep the line is.
• They can be increasing (positive gradient) or decreasing (negative gradient).
• They can be horizontal (zero gradient).
• They can be vertical (gradient is undefined).
• They have $x$x intercepts, $y$y intercepts or both an $x$x and a $y$y intercept.
• The gradient can be calculated using $\frac{\text{rise }}{\text{run }}$rise run ​ or $\frac{y_2-y_1}{x_2-x_1}$y2​−y1​x2​−x1​​.
• They have an equation of the form $y=mx+b$y=mx+b.

 

The values of $m$m and $b$b mean specific things. Explore for yourself what these values do by exploring on this interactive.

 

Gradient

So what you will have found is that the $m$m value affects the gradient.

• If $m<0$m<0, the gradient is negative and the line is decreasing
• if $m>0$m>0, the gradient is positive and the line is increasing
• if $m=0$m=0 the gradient is $0$0 and the line is horizontal
• Also, the larger the value of $m$m the steeper the line

Y-Intercept

We also found that the $b$b value affects the $y$y intercept.  

• If $b$b is positive then the line is vertically translated (moved) up.
• If $b$b is negative then the line is vertically translated (moved) down.

 

 

Question 1

$y=3x$y=3x

a) What is the the gradient?  The gradient is the value of the coefficient, (the number in front of the $x$x).

The gradient of this line is 3.

b) What is the $y$y-intercept?  The $y$y-intercept is the value of the constant term, (the number on its own).  The $y$y-intercept of this line is 0.  

 

Question 2

$y=-2x$y=−2x

• gradient is $-2$−2
• $y$y intercept is $0$0

 

Question 3

$y=\frac{x}{2}-3$y=x2​−3

• gradient is $\frac{1}{2}$12​
• $y$y intercept is $-3$−3

 

 

Question 4

 

Question 5

$2y=-4x+10$2y=−4x+10

First we need to rewrite it in the form or $y=mx+b$y=mx+b.

$y=-2x+5$y=−2x+5

• gradient is $-2$−2
• $y$y intercept is $5$5