Question

Equation of a line with an slope of 1/2 that contains (-4, 7)

Answer 1

Equation of a line with an slope of 1/2 that contains (-4, 7) is $y=\frac{1}{2} x+9$

Solution:

We have been given a point and slope of an equation and have been asked to write it in an equation. The two forms of writing a point and slope in equation are point slope form and standard form.

The standard form of a line is in the form Ax + By = C where A is a positive integer, and B, and C are integers. The standard form of a line is just another way of writing the equation of a line.

To write in standard form we will first write it in point slope form and then rearrange it into a standard from.

The formula for point slope form:

$y-y_{1}=m\left(x-x_{1}\right)$

where "m" is the slope of line

Given that "m" = $\frac{1}{2}$ and $(x_1, y_1) = (-4, 7)$

$\begin{array}{l}{y-7=\frac{1}{2}(x-(-4))} \\\\ {y-7=\frac{1}{2}(x+4)} \\\\ {y-7=\frac{1}{2} x+2} \\\\ {y=\frac{1}{2} x+9}\end{array}$

Now, let us convert this equation to standard form

0.5x + 9 = y

0.5x - y = -9

Thus we have found out equation of line in point slope and standard form