Question

write an equation of the line, in slope intercept form, which passes through the given point and is parallel to the given line. 6. (1, 2); y = -5x + 4 7. (2, -5); 2y = 3x + 10

Explanation:

Problem 6:

Step1: Recall slope of parallel lines

Parallel lines have equal slopes. The given line is \( y = -5x + 4 \), so its slope \( m = -5 \).

Step2: Use point - slope form

The point - slope form of a line is \( y - y_1 = m(x - x_1) \), where \( (x_1,y_1)=(1,2) \) and \( m=-5 \).
Substitute the values: \( y - 2=-5(x - 1) \)

Step3: Convert to slope - intercept form

Expand the right - hand side: \( y - 2=-5x + 5 \)
Add 2 to both sides: \( y=-5x+5 + 2=-5x + 7 \)

Step1: Find the slope of the given line

First, rewrite the given line \( 2y = 3x+10 \) in slope - intercept form (\( y=mx + b \)) by dividing both sides by 2: \( y=\frac{3}{2}x + 5 \). So the slope \( m=\frac{3}{2} \).

Step2: Use point - slope form

The point is \( (2,-5) \) and \( m = \frac{3}{2} \). The point - slope form is \( y - y_1=m(x - x_1) \).
Substitute \( x_1 = 2,y_1=-5 \) and \( m=\frac{3}{2} \): \( y-(-5)=\frac{3}{2}(x - 2) \), which simplifies to \( y + 5=\frac{3}{2}(x - 2) \)

Step3: Convert to slope - intercept form

Expand the right - hand side: \( y+5=\frac{3}{2}x-3 \)
Subtract 5 from both sides: \( y=\frac{3}{2}x-3 - 5=\frac{3}{2}x-8 \)

Answer:

\( y=-5x + 7 \)

Problem 7: