The equation of a line given two points needs to be found. Samuel claims that slope-intercept form will generate the equation an

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15 days ago

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The equation of a line given two points needs to be found. Samuel claims that slope-intercept form will generate the equation an

d Helena claims that point-slope form will find the equation. Who is correct? Explain your reason by describing both forms.

Mathematics

2 answers:

tester [3.8K] · Answer 1 · 2026-02-18T12:53:12+03:00

Example Answer: Both approaches are valid. Each form will lead to the identical line equation. The slope-intercept form calculates the y-intercept from the slope and a point. Meanwhile, point-slope form determines the equation by using the slope and a specific point to solve for y.

Svet_ta [4.2K] · Answer 2 · 2026-02-18T12:56:55+03:00

Helena is right in stating that the point-slope form can produce the line's equation. This form is expressed as:

y - y₁ = m(x - x₁), where,
m = (y₂ - y₁) / (x₂ - x₁) represents the slope of the line
(x₁, y₁) and (x₂, y₂) denote the coordinates of the two given points.

Conversely, the slope-intercept form looks like this:

y = mx + b, where,
m is the slope
b stands for the y-intercept

Since only two points are provided here, the y-intercept is unknown at first glance. Therefore, the equation can be found using the point-slope form, which just needs the known coordinates substituted into the formula.
Given two points, one must find the equation of the line. Samuel believes using the slope-intercept form is correct, while Helena thinks point-slope form is appropriate. Who has the right answer? Explain by discussing each method.