Find an equation of the line that șatisfies the given conditions. Through $$ (3,7) $$ and $$ (2,9) $$

Question

UpStudy AI · Accepted Answer

To find the equation of the line that passes through the points $$ (3, 7) $$ and $$ (2, 9) $$, follow these steps:

### 1. Calculate the Slope ($$ m $$)

The slope of a line passing through two points $$ (x_1, y_1) $$ and $$ (x_2, y_2) $$ is given by:

$$
m = \frac{y_2 - y_1}{x_2 - x_1}
$$

Plugging in the given points:

$$
m = \frac{9 - 7}{2 - 3} = \frac{2}{-1} = -2
$$

### 2. Use the Point-Slope Form

With the slope $$ m = -2 $$ and using one of the points, say $$ (3, 7) $$, the point-slope form of the equation is:

$$
y - y_1 = m(x - x_1)
$$

$$
y - 7 = -2(x - 3)
$$

### 3. Convert to Slope-Intercept Form ($$ y = mx + b $$)

Expand and simplify the equation:

$$
y - 7 = -2x + 6
$$

$$
y = -2x + 6 + 7
$$

$$
y = -2x + 13
$$

### **Final Equation**

$$
\boxed{y = -2x + 13}
$$
The equation of the line is $$ y = -2x + 13 $$.

Find an equation of the line that șatisfies the given conditions. Through \( (3,7) \) and \( (2,9) \)