This document discusses different forms of linear equations including the general form (ax + by + c = 0), slope-intercept form (y = mx + b), point-slope form (y-y1 = m(x-x1)), and two-point form (y-y1 = y2-y1(x-x1)/(x2-x1)). It also discusses key concepts such as parallel lines which are always the same distance apart and do not intersect, perpendicular lines which intersect at a 90 degree angle, and intercepts which are the points where a line crosses the x or y-axis. The document contains questions about determining equations of lines and finding missing vertices of geometric shapes.

1. Applications of Co-Ordinate
Geometry
LESSON 7

2. FORMS OF LINEAR EQUATION
1.ax + by + c= 0 general form
2.y = mx + b slope-intercept form
3.y-y1 = m(x-x1) point-slope form
4.y-y1 = y2-y1 (x-x1) two- point form
x2-x1

3. Component 1: Short Review
Questions
Q1. What is the gradient of the line y = 3x − 7?
Q2. What is the y-intercept of the line y = 3x − 7?
Q3. Rewrite the equation of the line y = 3x − 7 in the form ax+ by + c = 0
Q4. Write an equation of a line parallel to of the line y = 3x − 7
Q5. Graph the line y = 3x − 7 on a number plane and then graph your line from Q4.

4. KEY CONCEPTS
Parallel Lines – are
lines in a plane that
are always the same
distance apart, do not
intersect.

5. KEY CONCEPTS
Perpendicular Lines –
are lines that intersect
at a right (90 degrees)
angle.

6. KEY CONCEPTS
Intercept – is the point where
the line crosses the x-axis, called
the X-INTERCEPT, and the point
where theline crosses the y-axis,
called the Y-INTERCEPT.

8. Component 4B
Q1. Determine the
equations for all three
lines. Give answers in
the form ax + by + c =
0.

11. Component 4C
Q1. A square has vertices at (0, 0)
and (2, 0). Where are the other 2
vertices? (There is more than
one possible answer.)

12. Q2. An
equilateral
triangle has
vertices at (0, 0)
and (2, 0). Where
is the other
vertex? (There
are 2
possible
answers.)

13. Q3. A parallelogram has
vertices at (0, 0), (2, 0).
and (1, 1). Where is the
other vertex?