Write an equation of the line passing through the points (4,12) and (−1,−13).

Step-by-step explanation:

For us to write the equation for this line, we need to (1) find the slope of the line, and (2) use one of the points to write an equation:

The question gives us two points, (4,12) and (−1,−13), from which we can find the slope and later the equation of the line.

Finding the Slope  

The slope of the line (m) = (y₂ - y₁) ÷ (x₂ - x₁)  

                                          =  (12 - (- 13)) ÷ (4 - (- 1))

                                          =   25  ÷  5

                                         =  5

Finding the Equation

We can now use the point-slope form (y - y₁) = m(x - x₁)) to write the equation for this line; where (x₁ , y₁) = (4, 12):

    we could also transform this into the slope-intercept form ( y = mx + c)

                   since y - 12 = 5 (x - 4)

                              y - 12 =  5x + 5 (-4)

                                    y = 5x - 20 + 12

To test my answer, I have included a Desmos Graph that I graphed using the information provided in the question and my answer.

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step-by-step explanation:

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proofs involving isosceles triangles often require special consideration because an isosceles triangle has several distinct properties that do not apply to normal triangles.(more about triangle types) therefore, when you are trying to prove that two triangles are congruent, and one or both triangles, are isosceles you have a few theorems that you can use to make your life easier.

step-by-step explanation:

an isosceles triangle has two congruent sides and two congruent angles. the congruent angles are called the base angles and the other angle is known as the vertex angle. ∠bac and ∠bca are the base angles of the triangle picture on the left. the vertex angle is ∠abc