In the diagram, line l and line m are parallel, m4 = 7x + 5 and m5 = 5x + 27. Solve for the value of angle 4.

Step-by-step explanation:

First, when determining the equation of a linear equation, always try and find the slope first.

To find the slope, we can use the slope formula:

Where (x₁, y₁) and (x₂, y₂) are two points.

So, let’s pick two points from the table. It doesn’t matter which two we pick. I’m going to use (30, 140) and (45, 185).

While it doesn’t matter which two we pick, it does matter how we orient them in our formula. Let (30, 140) be (x₁, y₁) and (45, 185) be (x₂, y₂). Substitute them carefully. This should yield:

Evaluate. Subtract and divide:

Now, we can use the point-slope form. The general formula is:

Where m is the slope and (x₁, y₁) is a point.

So, let’s substitute 3 for m. This yields:

For our point, any one of our five points can be used. Again, it’s more important that you put the values in the correct positions.

Let’s use the first point (30, 140). So, let (30, 140) be (x₁, y₁). This yields:

Since the question asks us to leave them in point-slope form, we are done!

And, for reference, here are the four other, equivalent forms:

All of the above, including the previous one, are valid answers.