In the image below, moving the points $A$ and $B$ on the line will not change the gradient between them.

This is the key to finding the equation of a straight line. On the next page, we're going to develop and use the point-slope formula which gives the equation of a straight line quickly and conveniently.

1. Find the equation of the straight line with gradient $3$ passing through the point $(2,5)$, giving your answer in the form

   $$y=mx+c$$

   State the $x$ and $y$ intercepts of this line.

2. Find the equation of the straight line which passes through the points

   $$(-2,3)\text{and}(5,7)$$

   giving your answer in the form

   $$ax+by+c=0$$