Linear Equations
UK Secondary (7-11)
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Identifying Slope from Equation
Lesson

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 $\frac{y_2-y_1}{x_2-x_1}$y2y1x2x1.
  • 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=x23

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

 

 
Question 4

Consider the equation $y=-1-\frac{9x}{2}$y=19x2.

  1. State the gradient of the line.

  2. State the $y$y-value of the $y$y-intercept.

 

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

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