Point-slope form: y minus y 1 = m (x minus x 1).

Question

Use the point-slope form of a line to write the equation of a line that has a slope of 2 and passes through the point (–4, 3). Write the equation in slope-intercept form.

Choose the equation of the line.

y = 2x – 7
y = 2x + 11
y = –4x + 14
y = 3x +14

Answer 1

To use the point-slope form equation \(y - y_1 = m(x - x_1)\), we can substitute the values from the problem:

• Slope \(m = 2\)
• Point \((x_1, y_1) = (-4, 3)\)

Substituting these into the point-slope form equation:

\[ y - 3 = 2(x - (-4)) \]

This simplifies to:

\[ y - 3 = 2(x + 4) \] \[ y - 3 = 2x + 8 \]

Now, we add 3 to both sides to convert it to slope-intercept form \(y = mx + b\):

\[ y = 2x + 8 + 3 \] \[ y = 2x + 11 \]

So, the equation of the line in slope-intercept form is:

\[ y = 2x + 11 \]

The correct choice from the options provided is:

y = 2x + 11