Question

The equation of a line given two points needs to be found. Samuel claims that slope-intercept form will generate the equation and Helena claims that point-slope form will find the equation. Who is correct? Explain your reason by describing both forms.

Answer 1

According to the question, Samuel claims that the slope-intercept form will generate the required equation. At the same time, Helena claims that the point-slope form will generate the same.

Both the slope-intercept form & the point-slope form are correct. If one uses either of them, it will lead to the same equation. The slope-intercept form, suggested by Samuel, utilises the slope and a point to get the y-intercept. Similarly, the point-slope form, proposed by Helena, also uses the slope and a point to solve for y, and hence generate the required equation.

Answer 2

Helena claims that point-slope form will find the equation.

Helena is correct.

Step-by-step explanation:

Equation of a line in slope-intercept form is

$y=mx+c$

where m is the slope and c is the intercept of the line on y-axis

Also, the equation of a line in point-slope form is

$y-y_1=m(x-x_1)$

Where $(x_1,y_1)$ is the point and m is the slope.

Since the slope of a line passing through two points can be found out using

$m=\frac{y_2-y_1}{x_2-x_1}$

Therefore, we can find out the equation of the line using point-slope form.

Therefore, Helena is correct since we cannot find out the intercept c and hence Samuel's method is incorrect,

Hope this answer is helpful.

Know More:

Q: What is the equation in point-slope form and slope intercept form for the line given slope= 8/3,(-2,-6)?

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