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The point-slope form of the equation of the line that passes through (–9, –2) and (1, 3) is y – 3 = one-half EndFraction(x – 1). What is the slope-intercept form of the equation for this line?

y = y equals StartFraction one-half EndFraction x plus 2.x + 2
y = y equals StartFraction one-half EndFraction x minus 4.x – 4
y = y equals StartFraction one-half EndFraction x plus StartFraction 5 Over 2 EndFraction.x +
y = y equals StartFraction one-half EndFraction x minus StartFraction 7 Over 2 EndFraction.x –

1 answer

To find the slope-intercept form of the equation of the line, we start with the point-slope form given:

\[ y - 3 = \frac{1}{2}(x - 1) \]

We will rearrange this equation into slope-intercept form, \( y = mx + b \), where \( m \) is the slope and \( b \) is the y-intercept.

  1. Distribute \( \frac{1}{2} \) on the right side:

    \[ y - 3 = \frac{1}{2}x - \frac{1}{2} \]

  2. Next, add 3 to both sides to isolate \( y \):

    \[ y = \frac{1}{2}x - \frac{1}{2} + 3 \]

  3. Combine the constant terms on the right side:

    \[ -\frac{1}{2} + 3 = -\frac{1}{2} + \frac{6}{2} = \frac{5}{2} \]

So we have:

\[ y = \frac{1}{2}x + \frac{5}{2} \]

Thus, the slope-intercept form of the equation of the line is:

\[ y = \frac{1}{2}x + \frac{5}{2} \]

So the correct answer is:

\( y = \frac{1}{2}x + \frac{5}{2} \)