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substitute the known values of m, x₁, and y₁ into the above point - slope form of the equation.
point - slope form of
line cz
y - y₁ = m(x - x₁)
y - y₁ = \frac{3}{2}(x - x₁)

Question

Accepted Answer

To solve this, we need to substitute the known values of $ m $, $ x_1 $, and $ y_1 $ into the point - slope form $ y - y_1=m(x - x_1) $. From the given equation $ y - y_1=\frac{3}{2}(x - x_1) $, we can see that the slope $ m=\frac{3}{2} $. But since the problem just asks to substitute the known values (even though the specific values of $ x_1 $ and $ y_1 $ are not fully shown here, the general process is as follows):

### Step 1: Identify the values
Let's assume we have a point $ (x_1,y_1) $ and slope $ m = \frac{3}{2} $. The point - slope form is $ y - y_1=m(x - x_1) $.

### Step 2: Substitute the values
If we have a specific point, say for example, if $ x_1 = a $ and $ y_1 = b $, we would substitute them into the equation. So the equation becomes $ y - b=\frac{3}{2}(x - a) $.

Since the problem is about substituting into the point - slope form and we know that $ m=\frac{3}{2} $, and we just need to put in the values of $ x_1 $ and $ y_1 $ (which are likely given in the original problem context that is not fully shown here) into the formula $ y - y_1=\frac{3}{2}(x - x_1) $.

If we assume that maybe there was a typo and $ x_1 $ and $ y_1 $ are specific numbers, for example, if $ x_1 = 2 $ and $ y_1 = 3 $, the equation would be $ y - 3=\frac{3}{2}(x - 2) $. But in general, the process is to take the known $ x_1 $, $ y_1 $ and $ m=\frac{3}{2} $ and plug them into $ y - y_1=m(x - x_1) $.

If we consider the form of the equation after substitution (assuming that the values of $ x_1 $ and $ y_1 $ are just represented as they are in the problem), the equation with $ m = \frac{3}{2} $ substituted is $ y - y_1=\frac{3}{2}(x - x_1) $.

If we were to expand this equation (for the purpose of maybe getting it into slope - intercept form), we would do the following:

### Step 3: Expand the equation (optional, if needed)
$$
\begin{align*}
y - y_1&=\frac{3}{2}x-\frac{3}{2}x_1\
y&=\frac{3}{2}x-\frac{3}{2}x_1 + y_1
\end{align*}
$$

But since the problem is about substitution, the main thing is to put the known $ m=\frac{3}{2} $, $ x_1 $ and $ y_1 $ into the point - slope formula.

If we assume that the problem is just to show the substitution of $ m=\frac{3}{2} $ into the point - slope form, then the equation after substitution is $ y - y_1=\frac{3}{2}(x - x_1) $ (and if we have numerical values for $ x_1 $ and $ y_1 $, we can substitute them as well).

If we consider a common example, let's say the point is $ (2,4) $ (this is just an example to show the substitution process), then:

### Step 1: Identify values
$ x_1 = 2 $, $ y_1 = 4 $, $ m=\frac{3}{2} $

### Step 2: Substitute into point - slope form
$ y-4=\frac{3}{2}(x - 2) $

### Step 3: Simplify (optional)
$$
\begin{align*}
y-4&=\frac{3}{2}x-3\
y&=\frac{3}{2}x + 1
\end{align*}
$$

If we are just asked to present the equation after substituting $ m=\frac{3}{2} $ (without specific $ x_1 $ and $ y_1 $ values), the equation is $ y - y_1=\frac{3}{2}(x - x_1) $

If we assume that the problem had a typo and $ x_1 $ and $ y_1 $ are supposed to be numbers (for example, if $ x_1 = 1 $ and $ y_1 = 1 $ just for illustration), then the equation would be $ y - 1=\frac{3}{2}(x - 1) $

The general answer after substitution (with $ m=\frac{3}{2} $) is $ y - y_1=\frac{3}{2}(x - x_1) $ (and if specific values of $ x_1 $ and $ y_1 $ are provided, we can substitute them to get a more specific equation)

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QUESTION IMAGE

Question

Explanation:

Step 1: Identify the values

Step 2: Substitute the values

Step 3: Expand the equation (optional, if needed)

Step 1: Identify values

Step 2: Substitute into point - slope form

Step 3: Simplify (optional)

Answer: