Question

Use the given conditions to write an equation for the line in point-slope form and general form.
Passing through (-7,9) and parallel to the line whose equation is 7x - 4y - 9 = 0
The equation of the line in point-slone form is

Answer 1

Answer:

(y - 9) = 7/4(x + 7)

Step-by-step explanation:

If two lines are parallel to each other, they have the same slope slopes.

The first line is 7x - 4y - 9 = 0.

First let's convert this to y = mx + b form.

• 7x - 4y - 9 = 0

Add 4y to both sides.

• 7x - 9 = 4y

Divide each term by 4.

• y = 7/4x - 9/4

The slope is 7/4. A line parallel to this one will also have a slope of 7/4.

The standard point-slope form is:

• (y - y₁) = m(x - x₁)

For the point-slope form, you need two things: a point and a slope.

• point: (-7, 9)
• slope: 7/4.

Plug in our given information.

• (y - 9) = 7/4(x - (-7))

Simplify.

• (y - 9) = 7/4(x + 7)

Learn with another example.

https://brainly.com/question/26681302

Hope this helps!

Answer 2

Let's consider the information given:

• line passes through (-7,9)
• line is parallel to 7x - 4y - 9 = 0

What do we want to solve: put the equation of the line in point-slope form

 ⇒ point-slope form ⇒ $y-y_{0}=m(x-x_{0} )$

• $(x_{0} ,y_{0} )$ : any point on the line
• m: slope

1.  Find the slope of 7x - 4y = 9

              ⇒ first put it into slope-intercept form $y = mx +b$

                         -where m is the slope and b is the y-intercept

                                 $7x-4y-9=0\\7x-4y=9\\-4y=-7x+9\\y=\frac{7}{4}x-\frac{9}{4}$

               ⇒ Slope is 7/4

     2. When two lines are parallel, their two slopes are equal, and since

         the line passes through (-7,9), use point-slope form

                $y-9=\frac{7}{4}(x+7)$ <== point-slope form

What do we also want: find the general form ⇒ Ax + By = C

• A: coefficient of x
• B: coefficient of y
• C: constant

1. To find the general form, move all the variables to one side and the  constant to the other, using the point-slope form

               $y-9=\frac{7}{4}(x+7)\\ y-9=\frac{7}{4}x+\frac{49}{4} \\-\frac{7}{4}x+y=9+\frac{49}{4} =\frac{36}{4} +\frac{49}{4} =\frac{85}{4} \\-\frac{7}{4}x+y=\frac{85}{4}$<== general form

Hope that helps!