Question 2 of 10

Identify an equation in slope-intercept form for the line parallel to [tex][tex]$y = 4x - 9$[/tex][/tex] that passes through [tex][tex]$(-5, 3)$[/tex][/tex].

A. [tex][tex]$y = 4x - 23$[/tex][/tex]

B. [tex][tex]$y = \frac{1}{4}x + 4 \frac{1}{4}$[/tex][/tex]

C. [tex][tex]$y = 4x + 23$[/tex][/tex]

D. [tex][tex]$y = -4x + 7$[/tex][/tex]



Answer :

To identify an equation in slope-intercept form for the line parallel to [tex]\( y = 4x - 9 \)[/tex] that passes through the point [tex]\((-5, 3)\)[/tex], follow these steps:

1. Identifying the Slope of the Parallel Line:
Lines that are parallel have the same slope. The slope of the given line [tex]\( y = 4x - 9 \)[/tex] is [tex]\( 4 \)[/tex]. Thus, the slope of our new line will also be [tex]\( 4 \)[/tex].

2. Using the Point-Slope Form of the Equation:
The point-slope form of a line's equation is given by:
[tex]\[ y - y_1 = m(x - x_1) \][/tex]
where [tex]\( m \)[/tex] is the slope, and [tex]\((x_1, y_1)\)[/tex] is the point through which the line passes.

In this case, [tex]\( m = 4 \)[/tex], [tex]\( x_1 = -5 \)[/tex], and [tex]\( y_1 = 3 \)[/tex].

3. Substituting the Values into the Point-Slope Form:
[tex]\[ y - 3 = 4(x - (-5)) \][/tex]

4. Simplifying the Equation:
[tex]\[ y - 3 = 4(x + 5) \][/tex]
Distribute the [tex]\( 4 \)[/tex]:
[tex]\[ y - 3 = 4x + 20 \][/tex]
Isolate [tex]\( y \)[/tex] by adding [tex]\( 3 \)[/tex] to both sides:
[tex]\[ y = 4x + 23 \][/tex]

Therefore, the equation in slope-intercept form for the line parallel to [tex]\( y = 4x - 9 \)[/tex] that passes through [tex]\((-5, 3)\)[/tex] is:
[tex]\[ \boxed{y = 4x + 23} \][/tex]

From the given choices, the correct answer is:
C. [tex]\( y = 4x + 23 \)[/tex]