Using the gradient and $y$y-intercept to sketch the graph of a line
If we know the gradient and the $y$y-intercept of a line, then we can state its equation or rule. A line with gradient $m$m and $y$y-intercept $c$c has equation $y=mx+c$y=mx+c.
$y=mx+c$y=mx+c
where $m$m is the gradient and $c$c is the $y$y-intercept
Here are some examples:
$y=2x+4$y=2x+4 has gradient $2$2 and $y$y intercept = $4$4
$y=-3x-7$y=−3x−7 has gradient $-3$−3 and $y$y intercept = $-7$−7
$y=\frac{1}{2}x+10$y=12x+10 has gradient $\frac{1}{2}$12 and $y$y intercept = $10$10
A quick method to sketch the graph of a line is to use the $y$y intercept as the starting point and then the gradient to find other points on the line.
Practice questions
Question 1
Plot the graph of the line whose gradient is $-3$−3 and passes through the point $\left(-2,4\right)$(−2,4).
- Loading Graph...
Question 2
Consider the linear equation $y=3x+1$y=3x+1.
State the $y$y-value of the $y$y-intercept of this line.
Using the point $Y$Y as the $y$y-intercept, sketch a graph of the equation $y=3x+1$y=3x+1.
Loading Graph...
Question 3
Sketch a graph of the line $y=\frac{1}{2}x-2$y=12x−2 using its gradient and $y$y-intercept.
- Loading Graph...
Horizontal and vertical lines
On horizontal lines, the $y$y-value is always the same for every point on the line. They have the form $y=k$y=k.
On vertical lines, the $x$x-value is always the same for every point on the line. They have the form $x=k$x=k.
Practice questions
Question 4
Draw a graph of the line $y=-3$y=−3.
- Loading Graph...
Question 5
Graph the line $x=-6$x=−6.
Plot the line represented by the given points on the number plane.
Loading Graph...