Let's recall the point-slope form of a linear function.

y - y_{1} = m (x - x_{1})

Here

m

is the slope and

(x_{1}, y_{1})

is a point on the line. We will now explore two methods to graph a line given in point-slope form.

First we need to identify the slope and the point in the given function.

y - y_{1} y - 1 = m (x - x_{1}) = \frac{3}{2} (x - 4)

We identified the point

(4, 1)

and a slope of

\frac{3}{2} .

Recall that the slope is the change in

y

divided by the change in

x .

m = \frac{3}{2} ⇓ \frac{Δ y}{Δ x} = \frac{3}{2}

We will now first plot the point

(4, 1) .

Then we will, as indicated by the slope, take a step of

2

units to the right and

3

units up to find a second point.

By drawing a line through the points we have our graph.

The second method is to use the given equation to find a second point. This is done by substituting an arbitrary

y -

or

x -

coordinate into the equation and solving for the other variable. Let's substitute

x = 8

and solve for

y .

y - 1 = \frac{3}{2} (x - 4)

$x = 8$

y - 1 = \frac{3}{2} (8 - 4)

▼

Solve for

y

Subtract term

y - 1 = \frac{3}{2} (4)

$\frac{a}{c} \cdot b = \frac{a \cdot b}{c}$

y - 1 = \frac{1 2}{2}

Calculate quotient

y - 1 = 6

$LHS + 1 = RHS + 1$

y = 7

We have found that the point

(8, 7)

is on the graph. Now we can plot our two points and connect them with a line to graph our function.

Exercise 35 Page 176

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