Equations of lines-- the line with slope 5 that passes though the point (-1,3) intersects the x-axis at a point. what are the coordinates of this point?

I don't know what you mean by finding the coordinates of this point, but I do know how to find the equation. You have to use point slope form in order to figure this out. The equation for that is as follows:

y - y₁ = m(x - x₁)

Step 1: Find y₁ and x₁ by looking at your point and picking out the x and y values.

x₁ = x
y₁ = y

So... x₁ = -1 and y₁ = 3

Step 2: Find the slope. In this case, the slope is given to us. 

slope (m) = 5

Step 3: Plug all information in point slope form and solve.

y - (-1) = 5(x - 3)
y + 1 = 5x - 15
   - 1           - 1

 y = 5x - 16
 
 y = 5x = 16 is your final answer.   

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