Question

why do we convert linear equations from standard form to slope-intercept form?

1. to solve for x
2. to make them easier to graph
3. to find the y-intercept
4. to eliminate fractions

Explanation:

Analyze standard form

Standard form is written as \(Ax + By = C\). This form is useful for finding intercepts but does not directly show the slope or the y-intercept.

Analyze slope-intercept form

Slope-intercept form is written as \(y = mx + b\). In this form, \(m\) represents the slope and \(b\) represents the y-intercept.

Evaluate the purpose of conversion

Converting to \(y = mx + b\) gives us the slope and y-intercept immediately. This makes plotting points and sketching the line much simpler.

Compare the given options

• Option 1: "To solve for x" is incorrect because we solve for \(y\) during conversion.
• Option 2: "To make them easier to graph" is correct because knowing the slope and y-intercept allows for quick graphing.
• Option 3: "To find the y-intercept" is partially true, but standard form can also find it, and graphing is the primary overall utility.
• Option 4: "To eliminate fractions" is incorrect because conversion often introduces fractions.

Answer:

• 1 To solve for x
• 2 To make them easier to graph (Correct answer)
• 3 To find the y-intercept
• 4 To eliminate fractions