Equation of a straight line
Watch this video to learn about the equation of a straight line.
The general equation of a straight line is:
\(y = mx + c\)
where m is the In a graph, the gradient is the steepness of the line. The greater the gradient, the greater the rate of change. and c is the The value of the y-coordinate when a graph crosses the y-axis. (where the straight line cuts the y-axis)
Example
Find the gradient and y-intercept for the straight line with equation \(y = 5x + 7\)?
Answer
\(m=5\)
\(c=7\) so y-intercept is (0, 7)
Try these example questions
Question
Find the gradient and y-intercept for the straight line with equation \(y = 2x + 3\)
\(m = 2\)
\(c = 3\) so y-intercept is (0, 3).
Question
Find the gradient and y-intercept for the straight line with equation \(y = 8x - 4\)
\(m = 8\)
\(c = -4\) so y-intercept is (0, -4).
Question
Find the equation of the straight line shown below.
To find the equation of a straight line we need to know the gradient and the y-intercept.
Looking at the graph, the straight line cuts the y-axis at (0, 3) therefore c = 3.
Remember that the A simple piece of arithmetic you type into a spreadsheet to perform a calculation. The plural of 'formula' is 'formulae'. to calculate the gradient is:
\(Gradient(m) = \frac{{vertical\,distance}}{{horizontal\,distance}}\)
Therefore \(m = \frac{3}{6} = \frac{1}{2}\)
Since the straight line shown above is a downward slope, then:
\(m = - \frac{1}{2}\)
So, the equation of the straight line is:
\(y = - \frac{1}{2}x + 3\)
Question
Find the equation of the straight line shown below.
y-intercept is (-3, 0) therefore c = -3
\(m = \frac{v}{h} = \frac{8}{7}\)
Therefore, the equation of the straight line is:
\(y = \frac{8}{7}x - 3\)
Question
Which of these lines in the above diagram are horizontal and which are vertical?
\(y = 6\)
\(x= 3\)
\(x = -4\)
\(y = -8\)
Horizontal lines:\(y =6\) and \(y = -8\).
Vertical lines:\(x=3\) and \(x= 4\).
