Question

What is an equation in point-slope form for the line that passes through the points (4,-1) and (-3,4)? Oy-3= (x+4) Oy+4= (2+3) Oy+4= (z+3) Oy-4=-(z+3)​

Answer 1

The point-slope form of a line is given by the equation $y - y_1 = m(x - x_1)$, where $(x_1, y_1)$ is a point on the line and $m$ is the slope of the line.

To find the equation of the line that passes through the points $(4, -1)$ and $(-3, 4)$, we first need to calculate the slope of the line. This is given by the formula $m = \frac{y_2 - y_1}{x_2 - x_1}$, where $(x_1, y_1)$ and $(x_2, y_2)$ are two points on the line. Using the given points, we have $m = \frac{4 - (-1)}{-3 - 4} = \frac{5}{-7} = -\frac{5}{7}$.

Next, we plug this value of the slope and one of the points on the line into the point-slope form to find the equation of the line. Using the point $(4, -1)$, we get:

$$y - (-1) = -\frac{5}{7}(x - 4) \Longrightarrow y + 1 = -\frac{5}{7}(x - 4)$$

This is the equation of the line in point-slope form that passes through the points $(4, -1)$ and $(-3, 4)$.

Answer 2

Answer: This is equivalent to the equation (Oy+4= (2+3).

Explanation:

To write an equation in point-slope form for the line that passes through the points (4,-1) and (-3,4), we first need to find the slope of the line. We can do this using the formula for slope:

Now that we know the slope of the line, we can write the equation in point-slope form. This form of the equation is:

where (x1, y1) is a point on the line, and m is the slope of the line. In our case, we know that (4, -1) is a point on the line, and the slope of the line is -5/7. Therefore, the equation in point-slope form for the line that passes through the points (4,-1) and (-3,4) is:

This is equivalent to the equation (Oy+4= (2+3).