Question

graph a line that contains the point (2, 2) and has a slope of $-\frac{7}{5}$.

Explanation:

Step1: Recall the slope formula

The slope \( m = \frac{\Delta y}{\Delta x} \), where \( \Delta y \) is the change in \( y \) and \( \Delta x \) is the change in \( x \). Given slope \( m = -\frac{7}{5} \), this means for a change in \( x \) (run) of \( 5 \), the change in \( y \) (rise) is \( -7 \), or for a run of \( -5 \), the rise is \( 7 \).

Step2: Start from the given point \((2, 2)\)

• First direction (run \( 5 \), rise \( -7 \)):
• Add \( 5 \) to the \( x \)-coordinate: \( 2 + 5 = 7 \)
• Add \( -7 \) to the \( y \)-coordinate: \( 2 - 7 = -5 \)
• So we get the point \( (7, -5) \)
• Second direction (run \( -5 \), rise \( 7 \)):
• Add \( -5 \) to the \( x \)-coordinate: \( 2 - 5 = -3 \)
• Add \( 7 \) to the \( y \)-coordinate: \( 2 + 7 = 9 \)
• So we get the point \( (-3, 9) \)

Step3: Plot the points and draw the line

Plot the points \((2, 2)\), \((7, -5)\), and \((-3, 9)\) (or any two of these points) on the coordinate plane and draw a straight line through them.

Answer:

To graph the line, start at the point \((2, 2)\). Using the slope \( -\frac{7}{5} \), move 5 units to the right and 7 units down to get the point \((7, -5)\), or 5 units to the left and 7 units up to get the point \((-3, 9)\). Then draw a straight line through these points (or \((2, 2)\) and either of the other two points). The key points to plot are \((2, 2)\), \((7, -5)\), and \((-3, 9)\) (or any two of these along with \((2, 2)\)) to represent the line with slope \( -\frac{7}{5} \) passing through \((2, 2)\).