Question

How do you find a standard form equation for the line with $$\left(-2,2\right)$$ and $$\left(0,5\right)$$?

Answer 1

Hint:
In the given question, we have been given the coordinates of two points. There is a line joining the two points. We have to find the standard form equation of that line joining the two points. For doing that, we are going to first represent the line in slope-intercept form and then turn that slope-intercept form to the standard form.

Formula Used:
We are going to use the formula of slope in this question, which is:
$$m={\displaystyle \frac{y_2-y_1}{x_2-x_1}}$$

Complete step by step answer:
The slope intercept form of an equation is:
$$y=mx+b$$
The given points of the line are $$\left(-2,2\right)$$ and $$\left(0,5\right)$$.
First, we are going to calculate the slope of the line.
$$m={\displaystyle \frac{5-2}{0-\left(-2\right)}}={\displaystyle \frac{3}{2}}$$
So, we can write the slope intercept form of the equation as:
$$y=\left({\displaystyle \frac{3}{2}}\right)x+b$$
Now, we need to find the y-intercept, i.e., the point where the ordinate has some value and the abscissa is zero.
Clearly, from the question we can tell that since $$\left(0,5\right)$$ is a point on the line, then it means that the y-intercept is $$5$$ as its corresponding abscissa is zero.
Hence, $$y=\left({\displaystyle \frac{3}{2}}\right)x+5$$
Now, we multiply both sides of equation by $$2$$ and simplify,
$$2y=3x+10$$

Thus, the standard form is $$3x-2y+10=0$$

Note:
So, for solving questions of such type, we first write what has been given to us. Then we write down what we have to find. In this question, we had to find the standard equation of a line with given endpoints. To solve that, we first represented it in slope-intercept form, and then we turned it into the standard form. But it is very important that we know the formulae of the concepts being used, as without that, we cannot solve the question, at all.