Determine the equation of the line which passes through the points (0,−8) and (7,0).

Fill in the blanks:

(a) The y-coordinate of a point on the x-axis is _________.

b) The x-coordinate is called as _________.

(c) The x-axis and Y-axis intersect at _________.

(d) If a point (x,y) ≠ (0,0) is in the third quadrant, then x + y has _________sign.

(e) If a point (x,y) lies above horizontal axis, then y is always _________.

(f) The point of intersection of x = y and x = −y is _________.

(g) The line y =4x +5 intersects y-axis at the point _________.

True or false?

(a) The equation of the x-axis is x =0.

(b) The line x =4 is parallel to Y-axis.

(c) The line y =8 is perpendicular to x-axis.

(d) The lines x = y and x = −y are perpendicular to each other.

(e) The lines x =9 and y =9 are perpendicular to each other.

(f) The graph of y = x² is a straight line.

(g) The line y =3x +4 does not intersect x-axis.

(h) In a rectangular coordinate system, the coordinate axes are chosen such that they form a pair of perpendicular lines.

Determine the equation of the line in each of the following graphs:

A point P has coordinates (7,10) in a coordinate system X′OX ↔ Y′OY. Suppose it has coordinates (10,7) in another coordinate system X′₁O₁X₁↔ Y′₁O₁Y₁ with X′OX || X′₁O₁X₁. Find the coordinates of O₁ in the system X′OX ↔ Y′OY.