Write the standard form equation of the line that passes through the point p and is parallel to the line l. p : (-1, 0) l : y = (8/3)x – (17/3) Write the standard form equation of the line passing through these two points. p1 : (0, -3) p2 : (3, -5) Graph the following equation

Let’s break down your questions step by step.

### 1. Standard Form Equation of the Line Parallel to Line l

First, we need to find the slope of the given line l, which is in slope-intercept form:

( y = frac{8}{3}x – frac{17}{3} )

Here, the slope (m) is ( frac{8}{3} ). Since parallel lines have the same slope, the slope of the line we need to find is also ( frac{8}{3} ).

Next, we can use the point-slope form of the equation of a line, which is:

( y – y_1 = m(x – x_1) )

Where ( (x_1, y_1) ) is the point p (-1, 0).

Substituting in the values:

( y – 0 = frac{8}{3}(x + 1) )

( y = frac{8}{3}x + frac{8}{3} )

To convert it to standard form ( Ax + By = C ), we will clear the fraction:

Multiply everything by 3:

( 3y = 8x + 8 )

Rearranging gives:

( -8x + 3y = 8 )

Multiplying through by -1, we get:

Let’s tackle your questions one by one.

1. Write the standard form equation of the line that passes through the point p and is parallel to the line l.

First, let’s identify the slope of the given line l, which is in slope-intercept form ( y = mx + b ). Here, the slope ( m ) is ( frac{8}{3} ).

Since the line we want is parallel, it will have the same slope. So, the slope of our desired line is also ( frac{8}{3} ).

Using the point-slope form of a line’s equation, which is ( y – y_1 = m(x – x_1) ), we can substitute ( p(-1, 0) ) into the equation:

[

y – 0 = frac{8}{3}(x + 1)

]

Expanding this gives:

[

y = frac{8}{3}x + frac{8}{3}

]

To convert this to standard form ( Ax + By = C ), we rearrange:

[

-frac{8}{3}x + y = frac{8}{3}

]

Multiply through by 3 to eliminate the fraction:

[

-8x + 3y = 8

]

We can multiply the entire equation by -1 to get:

[

8x – 3y = -8