Question

line zd is represented by the equation $y = -\frac{3}{4}x + \frac{7}{4}$. determine the equation, in slope - intercept form, of the line fw that is parallel to line zd and passes through the point $f(-4, 9)$. (there is also a table with columns: slope of line zd ($m_1$), slope of line fw ($m_2$), point - slope form of line fw ($y - y_1 = m(x - x_1)$) and a coordinate grid with points z, d, f marked.)

Explanation:

Step1: Find slope of ZD

The equation of line ZD is \( y = -\frac{3}{4}x + \frac{7}{4} \). In slope - intercept form \( y=mx + b \), the slope \( m_1 \) (slope of ZD) is \( -\frac{3}{4} \).

Step2: Determine slope of FW

Since line FW is parallel to line ZD, parallel lines have equal slopes. So the slope \( m_2 \) (slope of FW) is also \( -\frac{3}{4} \).

Step3: Use point - slope form

The point - slope form of a line is \( y - y_1=m(x - x_1) \), where \( (x_1,y_1)=(-4,9) \) and \( m = -\frac{3}{4} \). Substitute these values into the formula:
\( y - 9=-\frac{3}{4}(x - (-4)) \)
Simplify the equation:
\( y - 9=-\frac{3}{4}(x + 4) \)
To convert to slope - intercept form (\( y=mx + b \)):
First, distribute the \( -\frac{3}{4} \): \( y - 9=-\frac{3}{4}x-3 \)
Then, add 9 to both sides: \( y=-\frac{3}{4}x + 6 \)

Answer:

• Slope of Line ZD (\( m_1 \)): \( -\frac{3}{4} \)
• Slope of Line FW (\( m_2 \)): \( -\frac{3}{4} \)
• Point - Slope Form of Line FW: \( y - 9=-\frac{3}{4}(x + 4) \)
• Slope - Intercept Form of Line FW: \( y=-\frac{3}{4}x + 6 \)