Line g is shown on the graph. coordinate plane with line g that passes through the points negative 3 comma 2 and 0 comma 5

Question

What is the equation of the line in slope-intercept form that is perpendicular to line g and passes through the point (1, 3)? Show all necessary steps.

Answer 1

Line g passes through (-3,2) and (0,5).

First, find the slope.

1. The formula for slope is (y₂ - y₁)/(x₂ - x₁).
2. Applying this formula, we get (5 - 2)/[0 - (-3)].
3. The slope is therefore 3/3, which is equal to 1.

Second, solve for b.

1. Slope intercept form is y = mx + b, where b is a constant and m is the slope.
2. We can use any coordinates of any point on the line g to find b, and I will use (0,5) for this example.
3. Filling in the slope intercept form with these coordinates creates the equation 5 = 1(0) + b.
4. (I put a 1 when evaluating for b to show you where the slope is, but since 1x = x, I didn't put it in the final solution.)
5. Evaluating this equation gives us b = 5.

The equation of line g is y = x + 5.