Question

Use point-slope form to write the equation of a line that passes through the point left bracket (7,-16) with slope 3

(PLEASE HELP ON THIS GIVING 100 POINTS!!)

Answer 1

Answer: y + 16 = 3(x - 7)

Work Shown

`\text{y} - \text{y}_1 = \text{m}(\text{x} - \text{x}_1)\\\\\text{y} - (-16) = 3(\text{x} - 7)\\\\\text{y} + 16 = 3(\text{x} - 7)\\\\`

If the formula image doesn't show up, then please refresh the page.

If your teacher wanted you to solve for y, then follow these steps:

`\text{y} + 16 = 3(\text{x} - 7)\\\\\text{y} = 3(\text{x} - 7) - 16\\\\\text{y} = 3\text{x} + 3(-7) - 16\\\\\text{y} = 3\text{x} - 21 - 16\\\\\text{y} = 3\text{x} - 37\\\\`

This is of the form y = mx+b where m = 3 is the slope and b = -37 is the y intercept. Two points on this line are (0,-37) and (7,-16).

Answer 2

`\sf y + 16 = 3(x - 7)`

Explanation:

The point-slope form of a linear equation is given by:

`\sf y - y_1 = m(x - x_1)`

where
`\sf (x_1, y_1)` is a point on the line, and
`\sf m` is the slope.

In this case, the point
`\sf (7, -16)` is on the line, and the slope is
`\sf 3`.

Substitute these values into the point-slope form:

`\sf y - (-16) = 3(x - 7)`

`\sf y + 16 = 3(x - 7)`

So, the equation of the line in point-slope form is:

`\sf y + 16 = 3(x - 7)`