(a) The linear formula...
is in Standard Format...
Ax+By-C=0, neither A nor B equal zero and A is greater than zero.
The slope is -A/B.
The slope of the line perpendicular to such is its negative inverse...
The Slope-Intercept linear formula is...
m is the slope.
b is the y-intercept, value of y when x=0. It is provided as (0,-7).
Standard form is...
(b) m and n are 2 lines which pass trough the point of intersection of lines l and k (6,-3) is a point on m. Find the equation of m.
The two equations are...
We need to find where these two lines intersection. The easiest technique is elimination. For this, either variable must have the same coefficient in both equations. I choose y. Its coefficient in the first equation is 2, and the second is -1. Let's take the second equation.
Let's multiply both sides by 2...
Let's add this to the other equation...
Let's plug this into either equation to establish the value of y at the point of intersection. I randomly select the first...
Let's plug both values into the second equation to verify results...
The point of intersection is (4,1).
The other point of the equation is (6,-3).
We must first establish slope. This is the change-of-y divided by the change-of-x...
Point-slope formula is...
We will use either point. I randomly select the first, (4,1)...
Let's plug-in the other point, (6,-3), to verify the result...
(ii) Find the two possible equations of n, if the angle between m and n is 45 degrees.
(4,1) is one point. One line is on one side of the line, the other line on the other side.
The two lines of n are perpendicular to each other.
I will think about it. I do not know the answer, at this time.