Graph the line with slope \( -\frac{3}{4} \) passing through the point \( (-3,2) \)

To graph the line with a slope of \( -\frac{3}{4} \) that passes through the point \( (-3, 2) \), we can use the point-slope form of the equation of a line, which is given by: \[ y - y_1 = m(x - x_1) \] where \( m \) is the slope and \( (x_1, y_1) \) is a point on the line. Here, \( m = -\frac{3}{4} \) and \( (x_1, y_1) = (-3, 2) \). Substituting these values into the equation, we get: \[ y - 2 = -\frac{3}{4}(x + 3) \] Now, we can simplify this equation: 1. Distribute the slope on the right side: \[ y - 2 = -\frac{3}{4}x - \frac{3}{4} \cdot 3 \] \[ y - 2 = -\frac{3}{4}x - \frac{9}{4} \] 2. Add 2 to both sides to solve for \( y \): \[ y = -\frac{3}{4}x - \frac{9}{4} + 2 \] 3. Convert 2 to a fraction with a denominator of 4: \[ 2 = \frac{8}{4} \] 4. Now combine the fractions: \[ y = -\frac{3}{4}x - \frac{9}{4} + \frac{8}{4} \] \[ y = -\frac{3}{4}x - \frac{1}{4} \] Now we have the equation of the line in slope-intercept form: \[ y = -\frac{3}{4}x - \frac{1}{4} \] ### Graphing the Line 1. **Plot the point** \( (-3, 2) \) on the graph. 2. **Use the slope** \( -\frac{3}{4} \) to find another point. From \( (-3, 2) \): - Move down 3 units (because of the negative slope) and right 4 units: - From \( (-3, 2) \), moving down 3 gives \( (-3, -1) \) and moving right 4 gives \( (1, -1) \). - So, another point on the line is \( (1, -1) \). 3. **Draw the line** through the points \( (-3, 2) \) and \( (1, -1) \). ### Summary The line with slope \( -\frac{3}{4} \) passing through the point \( (-3, 2) \) can be graphed by plotting the points \( (-3, 2) \) and \( (1, -1) \) and drawing a straight line through them.