Question

Consider the line that passes through the point (3, -6) and has a slope of 4.

Part 1: Write the equation of this line using point-slope form. (2 points)
Part 2: Using your equation from part 1, rewrite this equation in slope-intercept form. Make sure to show all of your work. (2 points)
Part 3: Using your equation from part 2, rewrite this equation in standard form. Make sure to show all of your work. (2 points)

Answer 1

Point Slope form:
\[y - y1 = m(x - x1)\]Where y1 and x1 stand for the given x and y coordinates, and m is the slope.
So substitute the values in:
\[y - (-6) = 4(x - 3)\]\[y + 6 = 4(x - 3)\]

Answer 2

\[y + 6 = 4(x - 3)\]You want it in Slope-Intercept form:
\[y = mx + b\]So lets solve for y.
Distribute the 4.\[y + 6 = 4x - 12\]Subtract 6 from both sides.
\[y + 6 = 4x - 12\] -6 -6
Now you have:\[y = 4x - 18\]

Answer 3

Standard form is Ax + By = C where A can NEVER be a fraction, decimal, or a negative number.

Answer 4

So you have:

y = 4x - 18

Subtract 4x from both sides.

-4x + y = -18
^No negatives allowed. So we multiply everything by -1.
\[-1(-4x + y = -18)\]-1 So the standard form is: 4x - y = 18