Question

write an equation of the line in point slope form (y - y₁) = m(x - x₁) given that the line is parallel to y = 6x - 26 and the line passes through (5, 7). then convert it to slope-intercept form.
point-slope form:
y - 7 = 6 (x - 5)
slope-intercept form:
y = 6x - 3

Explanation:

Step1: Determine the slope

Parallel lines have the same slope. The line \( y = 6x - 26 \) is in slope - intercept form \( y=mx + b \), where \( m \) is the slope. So the slope \( m = 6 \).

Step2: Write point - slope form

The point - slope form is \( y - y_1=m(x - x_1) \), where \( (x_1,y_1)=(5,7) \) and \( m = 6 \). Substituting these values, we get \( y - 7=6(x - 5) \).

Step3: Convert to slope - intercept form

Start with \( y - 7=6(x - 5) \).
Expand the right - hand side: \( y - 7=6x-30 \).
Add 7 to both sides: \( y=6x - 30 + 7 \), which simplifies to \( y = 6x-23 \)? Wait, there is a mistake in the original answer. Let's recalculate:
From \( y - 7=6(x - 5) \), expand \( 6(x - 5)=6x-30 \). Then \( y=6x - 30 + 7=6x-23 \).

Answer:

Point - Slope Form: \( y - 7 = 6(x - 5) \) (correct)
Slope - Intercept Form: The correct slope - intercept form should be \( y=6x - 23 \) (the original \( y = 6x-3 \) is incorrect). The correct process is:

1. Point - slope form: Given \( (x_1,y_1)=(5,7) \) and \( m = 6 \), \( y - 7=6(x - 5) \).
2. Slope - intercept form:

• Expand \( y - 7=6x-30 \).
• Add 7 to both sides: \( y=6x-30 + 7=6x - 23 \).