Find the equation of the line in slope-intercept form:

Question

A line passes through the points P(-2, -3) and Q(3, -5). Find the equation of the line in slope-intercept form.

Answer 1

We can do this two ways. Both need us to find m.

m = (-3 - (-5))/(-2 - 3) = -2/5

Now, we can input either point and solve for b.

y = mx + b

-3 = (-2/5)(-2) + b

-3 = 4/5 + b

b = -3 4/5

y = (-2/5)x - 3 4/5

Or, we can use point slope form using either point.

y - y₁ = m(x - x₁)

y - (-5) = (-2/5)(x - 3)

y + 5 = (-2/5)x + 6/5

y = (-2/5)x - 3 4/5

Answer 2

This question requires that you know the equations for slope and know how to derive the y-intercept given a slope and a point.

Slope intercept form is y = mx + b

Let the line connecting points P and Q be called line PQ.

To set the equation of PQ in slope-intercept form we need two things, unsurprisingly it's the slope and the intercept.

The slope, m, is simple enough. To calculate slope given 2 points P and Q, we can say the slope is

m = (y_Q-y_P) / (x_Q - x_P) = (-5 - (-3) ) / (3 - (-2)) = (-2) / 5

For the intercept, we can realize that the slope is the change in y with an increase of 1 in the positive x direction. That is, every time we move right 1, we change the y -coordinate to add the slope and every time we move left 1, we change the y - coordinate to subtract the slope.

This being said, we can take either point P and Q and apply what we now know about slope to find the y-intercept, b.

Let us take the point P (-2, -3). We need to move right 2 to get to x = 0 so we can set up the equation as the following:

b = -3 + 2m where m = -2 / 5

This is b = y_P + m (x₀ - x_P) where x₀ is the x-coordinate for which we want to find the y-value. In this case, x₀ = 0 This equation is derived from point slope form which is y₀ - y₁ = m (x₀ - x₁)

b= -3 + 2(-2 / 5) = -3 - 4/5 = -19/5

So we can then set up the slope intercept form to be y = (-2 / 5) x -19/5