Write in slope-intercept form an equation of the line that passes through the given points. \( \begin{array}{ll}\text { 3. }(-3,0),(-2,3) & \text { 4. }(-6,10),(6,-10)\end{array} \)

### Problem 3 **Step 1. Find the slope \( m \).** Using the two points \((-3,0)\) and \((-2,3)\), the slope is given by \[ m = \frac{y_2 - y_1}{x_2 - x_1} = \frac{3 - 0}{-2 - (-3)} = \frac{3}{1} = 3. \] **Step 2. Use the point-slope formula.** The point-slope form is \[ y - y_1 = m(x - x_1). \] Using \((-3,0)\) as \((x_1, y_1)\) and \(m = 3\), \[ y - 0 = 3(x - (-3)) \quad \Longrightarrow \quad y = 3(x + 3). \] **Step 3. Write in slope-intercept form.** Expanding the equation: \[ y = 3x + 9. \] --- ### Problem 4 **Step 1. Find the slope \( m \).** Using the two points \((-6,10)\) and \((6,-10)\), the slope is: \[ m = \frac{-10 - 10}{6 - (-6)} = \frac{-20}{12} = -\frac{5}{3}. \] **Step 2. Use the point-slope formula.** Using the form \[ y - y_1 = m(x - x_1), \] and selecting the point \((-6,10)\), \[ y - 10 = -\frac{5}{3}(x - (-6)) \quad \Longrightarrow \quad y - 10 = -\frac{5}{3}(x + 6). \] **Step 3. Write in slope-intercept form.** First, expand the right-hand side: \[ y - 10 = -\frac{5}{3}x -\frac{5}{3}(6). \] Since \[ \frac{5}{3} \times 6 = 10, \] this becomes: \[ y - 10 = -\frac{5}{3}x - 10. \] Add \(10\) to both sides: \[ y = -\frac{5}{3}x. \] --- **Final Answers:** - For the points \((-3,0)\) and \((-2,3)\), the equation is \[ y = 3x + 9. \] - For the points \((-6,10)\) and \((6,-10)\), the equation is \[ y = -\frac{5}{3}x. \]