Albert Teen YOU ARE LEARNING:  Straight Line Graphs 2  # Straight Line Graphs 2 ### Straight Line Graphs 2

We can find the equation of a straight line by finding the gradient and the y-intercept.

1

The gradient tells us a couple of things about a line - what are they? 2

The direction of the slope is determined by the sign of the gradient.

A positive gradient rises from left to right. A negative gradient descends from left to right. 1

We can calculate the gradient of a straight line if we know two points on that line.

This is the line that passes through the points $(2,8)$ and $(0,2)$. 2

We need to find the difference in the $y$ coordinates and divide by the difference in the $x$ coordinates.

This is also known as $\frac{rise}{run}$. 3

What is the difference between the $y$ coordinates?  4

What is the difference in the $x$ coordinates?  5

We know that $m=\frac{6}{2}$ so what is the gradient of this line?  6

It doesn't matter which point we use first but we must be consistent with the two coordinates.

We used $\frac{8-2}{2-0}=\frac{6}{2}=3$ We could have used the points the other way round $\frac{2-6}{0-2}=\frac{-6}{-2}=3$. 7

We can use the formula to find the gradient of the line.

The gradient of the line is normally shown as $m$. 1

What is the gradient of the line which passes through the points $(-4,3)$ and $(2,0)$.  1

The standard form of the equation of a straight line is $y=mx+c$ where $m$ is the gradient and $c$ is the $y$ intercept. What is the $y$ intercept on this straight line graph?  2

This is the same line whose gradient we found to be $-0.5$. Now we know the $y$ intercept is $1$, what is the equation of the line.  What is the gradient of the line with equation $y-3x=5$? 1

Now we know that the straight line has standard equation $y=mx+c$

we can find the equation of a line given the gradient and one point. 2

This line passes through the point $(10,5)$ and has gradient $2$. The first step is to take the standard form of the equation and put in the gradient. Select the correct option.  3

We now have part of our equation $y=2x+c$. We can use the point coordinates to work out $c$ by substituting into our equation, $5=2\times 10+c$. What is $c$?  1

What is the equation of the line with gradient $7$ and passes through the point $(-4,-3)$?  1

Summary! The gradient of the line is denoted by a number.

A positive gradient rises from left to right. A negative gradient descends from left to right. 2

The larger the number in the gradient, the steeper the line.

A gradient of $0.5$ is quite shallow. A gradient of $5$ is steep. 3

A horizontal line has a gradient of $0$.

The line does not go up or down. 4

A vertical line has an infinite gradient.

The line only goes up. 5

We can calculate the gradient of a line if we know two points on that line.

The gradient of a line is normally shown by the letter $m$. 6

The standard equation of a straight line is $y=mx+c$

Here, $m$ is the gradient and $c$ is the $y$ intercept.

7

We can find the equation of a line with the gradient and one point here that is $-3$ and $(1,2)$.

We start the equation $y=-3x+c$. Substitute the point, $2=-3\times 1+c$ and $c=5$ so the full equation is $y=-3x+5$. 8

Sometimes the equation of a straight line needs to be rearranged to put it into standard form.

The line with equation $y-x=5$. Rearrange to leave $y$ on the left hand side, $y=x-5$ and this is standard form. The gradient is $1$ and the $y$ intercept is $-5$.