Question

directions: write an equation passing through the point that is parallel to the given equation. 5. (-4, -1); ( y = 2x + 4 ) 6. (8, 3); ( y = -\frac{1}{4}x + 7 )

Explanation:

Problem 5: $(-4, -1)$; $y = 2x + 4$

Step1: Determine the slope

Parallel lines have the same slope. The given equation is in slope - intercept form $y=mx + b$, where $m$ is the slope. For $y = 2x+4$, the slope $m = 2$.

Step2: Use point - slope form

The point - slope form of a line is $y - y_1=m(x - x_1)$, where $(x_1,y_1)$ is a point on the line and $m$ is the slope. Here, $x_1=-4$, $y_1 = - 1$ and $m = 2$.
Substitute these values into the point - slope form:
$y-(-1)=2(x - (-4))$
Simplify the left - hand side and the right - hand side:
$y + 1=2(x + 4)$

Step3: Convert to slope - intercept form

Expand the right - hand side: $y+1 = 2x+8$
Subtract 1 from both sides: $y=2x+8 - 1$
$y=2x + 7$

Problem 6: $(8, 3)$; $y=-\frac{1}{4}x + 7$

Step1: Determine the slope

Parallel lines have the same slope. The given equation $y =-\frac{1}{4}x + 7$ is in slope - intercept form $y=mx + b$, so the slope $m=-\frac{1}{4}$.

Step2: Use point - slope form

The point - slope form is $y - y_1=m(x - x_1)$, where $(x_1,y_1)=(8,3)$ and $m =-\frac{1}{4}$.
Substitute the values: $y - 3=-\frac{1}{4}(x - 8)$

Step3: Convert to slope - intercept form

Expand the right - hand side: $y-3=-\frac{1}{4}x+2$
Add 3 to both sides: $y=-\frac{1}{4}x+2 + 3$
$y=-\frac{1}{4}x+5$

Answer:

1. The equation is $y = 2x+7$
2. The equation is $y=-\frac{1}{4}x + 5$