Sheila needs to determine the equation of a line passing through the point -6,-2 that is perpendicular to y=2x-4

If a line is perpendicular to another, the slopes multiplied will equal -1. To find the slope of the other line, you would need to find a number that when multiplied by 2 equals to -1. The slope of the other line would be -1/2. Now your equation for the other line is y=-1/2x +b. To find b, or your y-intercept, plug in the points they give you, so -2=-1/2(-6)+b and solve for b. For the equation of the line you should get y=-1/2x -5

64°

Step-by-step explanation:

Let's answer the guiding questions:

"1. What kind of triangle is this?"

Since two of the triangle's legs are the same length, this is an isosceles triangle.

"2. What does that tell me about the angles?  Which two angles are congruent?"

Isosceles triangles have a vertex angle (the angle between the congruent sides) and two base angles.  The base angles are congruent.

"3. How can we use congruent angles and the triangle sum theorem to solve for x?"

Since we know the third angle is 58°, and that angles of a triangle add up to 180°, we can write and solve an equation.

x + 58° + 58° = 180°

x + 116° = 180°

x = 64°