Question

How to do a linear equation given the point and slope or two points (-4, 6); slope = 3/4

Answer 1

To write the linear equation with the given point (-4, 6) and slope 3/4, use the point-slope form to get y - 6 = (3/4)(x + 4), which simplifies to the standard linear form y = (3/4)x + 9.

Step-by-step explanation:

To write a linear equation given a point and slope, you can use the point-slope form of the equation of a line, which is y - y1 = m(x - x1), where (x1, y1) is the point and m is the slope. In your case, the point is (-4, 6) and the slope is 3/4. Plugging these values into the point-slope form gives you y - 6 = (3/4)(x + 4). To write this in the standard linear form, distribute the slope through the parentheses and move the constant term to the other side to get y = (3/4)x + 9.

Answer 2

`\sf y = (3)/(4)x + 9`

Step-by-step explanation:

To write the equation of a line given a point
`\sf (x_1, y_1)` and the slope
`\sf m`, we can use the point-slope form of a linear equation:

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

In this case, we have the point
`\sf (-4, 6)` and the slope
`\sf m = (3)/(4)`.

Substitute these values into the formula:

`\sf y - 6 = (3)/(4)(x - (-4))`

Now, simplify the equation:

`\sf y - 6 = (3)/(4)(x + 4)`

Distribute the
`\sf (3)/(4)` to both terms inside the parentheses:

`\sf y - 6 = (3)/(4)x + 3`

Now, add 6 to both sides of the equation to isolate
`\sf y`:

`\sf y = (3)/(4)x + 9`

So, the equation of the line with a slope of
`\sf (3)/(4)` and passing through the point
`\sf (-4, 6)` is
`\sf y = (3)/(4)x + 9`.