Question

Graph the line with a slope of −1 that contains the point (3,6).

Answer 1

The equation of the line is y = -1.x + 9

Graph is provided in the attached figure

Explanation:

The slope intercept equation of a line in 2D(x,y) coordinates is given by the equation

`y = mx + c`

where m is the slope of the line and c the y-intercept i.e. where the line crosses the y axis at x = 0

Given slope = -1, we can find c and the equation of the line

Since (3,6) is a point on the graph, these coordinates must satisfy the above equation

Substitute for y = 6 and x = 3

`6 = (-1)3 + c\\\\c = 9\\\\\textrm{Equation of line is }\\y = -1.x + 9 \\y = 9-x`

In the attached figure you can see that (3,6) is on the line