MHB What is the equation of a line passing through (6, -3) with a y-intercept of 8?

[mathdad]

Find an equation of the line passing through (6, -3) and has y-intercept 8. Express final answer in the form y = mx + b.

If it has y-intercept 8, this means the point (0, 8).

I now have 2 points.

1. Find the slope

2. Use the point-slope formula

3. Solve for y

Correct?

 

[MarkFL]

A line passing through the point:

$$\left(x_1,y_1\right)$$

And having the $y$-intercept $b$, expressed in slope intercept form, will be:

$$y=\frac{y_1-b}{x_1}x+b$$

 

[mathdad]

Is my information correct?

 

[MarkFL]

Is my information correct?

Essentially, although I would change step 3 to read "Arrange in slope-intercept form." It's not enough to just solve for y, because we could have solved for y but not used the slope-intercept form, such as:

$$y=m(x-a)+b$$

We would want to arrange this as:

$$y=mx+(b-ma)$$

 

[mathdad]

By solving for y I meant slope-intercept form y = mx + b.