Question

Write the equation for a line that is parallel to the line y=5-2/3x and passes through the point (-3,0)

Answer 1

The equation of the line parallel to
`y = 5 - \((2)/(3)\)x` and passing through the point (-3,0) is
`y = -\((2)/(3)\)x + 2.`

Step-by-step explanation:

To write the equation of a line that is parallel to the given line
`y = 5 - \((2)/(3)\)x` and passes through the point (-3,0), we first identify the slope of the given line. The slope (m) of the line
`y = 5 - \((2)/(3)\)x` is \(-\frac{2}{3}\). Since parallel lines have the same slope, our new line will also have the slope of
`\(-(2)/(3)\)`. Using the point-slope form of a line's equation, which is y - y1 = m(x - x1), where (x1, y1) is a point on the line and m is the slope, we substitute m with
`\(-(2)/(3)\)` and
`(x_1, y_1)` with (-3,0):

`y - 0 = -\((2)/(3)\)(x - (-3))`

Simplifying, we get:

`y = -\((2)/(3)\)x + 2`

This is the equation of the line parallel to
`y = 5 - \((2)/(3)\)x` passing through the point (-3,0).

Answer 2

y=-2/3x-2

Step-by-step explanation:

Lines that are parallel to each other have the same slope. The line you start with is in the form y = mx + b, with an m, or slope, of -2/3. This means that The other line will also have a slope of -2/3. To make the line touch the point however, you must add a b so that it lands where you want it. If you have the equation y = -2/3x, and plug in -3, you get 2 for y, however we want 0. Therefore, we need to have a b of -2. This gives us a final equation of y = -2/3x - 2