a) Identify the slope and y-intercept −4(y − 4) = 3(x − 2) b) Given the point (-6, 7) and a slope of ½ , write the equation of a line:

Answer 1

In part a) of your question, we need to divide both sides of the equation by -4 in order to obtain the equation:

y - 4 = -3/4(x-2).

We can now distribute the -3/4 so that the equation becomes y - 4 = -3/4*x + 3/2. Then, we can add 4 to both sides:

y = -3/4 * x + 11/2.

Recall that this is known as the slope-intercept form: y = mx + b where m is the slope and b is the y-coordinate of the y-intercept. So, your slope is -3/4 and your y-intercept is (0 , 11/2)

For part b), recall that one way of writing the equation of a line is called point-slope form. It is called this because all you need to determine the equation of the line is a single point and the line's slope. In general the formula looks like this:

y - y₁ = m(x - x₁) where (x₁ , y₁) is your point and m is your slope.

Since part b) already gives you a point and a slope, we can just plug in all that information into the point-slope formula:

y - 7 = 1/2(x+6)

Answer 2

Hi Justin,

for question a. distribute out the equation first. -4 y +16 = 3 x -6

then isolate the y variable by adding the additive inverse of 16

so then we have -4 y = 3 x -22

divide everything by - 4 . slope is -3/4 and y intercept is 22/4

for b. using y= m x + b

substitute in ( -6, 7) and slope of 1/2

7 = 1/2 ( -6) + b

b= 10

equation is then what ? you have the slope and the b intercept.

Hope this helps.