MHB I have a few more questions.No problem, happy to help!

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To find the equation of the line passing through the point (6, -3) with a y-intercept of 8, the y-intercept can be represented as the point (0, 8). The slope is calculated using the formula m = (y2 - y1) / (x2 - x1), resulting in m = -11/6. Substituting this slope and the y-intercept into the point-slope formula yields the equation y = -11/6x + 8. This confirms the line's equation is y = -11/6x + 8, aligning with the initial conditions provided.
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Find an equation of the line that passes through (6, -3) and has y-intercept 8.

The y-intercept 8 can be expressed as the point (0, 8).

Correct?

I then find the slope of (6, -3) and (0, 8).

Yes?

The next step is to plug one of the above points and the slope into the point-slope formula and solve for y.

Is any of this right?
 
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RTCNTC said:
Find an equation of the line that passes through (6, -3) and has y-intercept 8.

The y-intercept 8 can be expressed as the point (0, 8).

Correct?

Correct.

RTCNTC said:
I then find the slope of (6, -3) and (0, 8).

Yes?

Yes.

RTCNTC said:
The next step is to plug one of the above points and the slope into the point-slope formula and solve for y.

An equation for a line is y = mx + b where m is slope and b is the y-intercept. To write the equation of your line in this form we need the slope and y-intercept. For the y-intercept, what does the fact that (0, 8) is on the line tell you when you substitute for x and y in your y = mx + b equation?
 
greg1313 said:
Correct.
Yes.
An equation for a line is y = mx + b where m is slope and b is the y-intercept. To write the equation of your line in this form we need the slope and y-intercept. For the y-intercept, what does the fact that (0, 8) is on the line tell you when you substitute for x and y in your y = mx + b equation?

When I substitute (0,8) into y = mx + b, the answer is b = 8.
This means the graph crosses the y-axis at the point (0,8).
 
(6,-3) & (0,8)

m = (8-(-3))/(0-6)

m = (8+3)/(-6)

m = -11/6

I will use (0,8).

y - 8 = (-11/6)(x - 0)

y - 8 = (-11x/6)

y = (-11x/6) + 8

Yes?
 
We are given that the line has $y$-intercept 8, so your line may be written as:

$$y=mx+8$$

Now, we are given the point on the line $(6,-3)$, and so substituting for $x$ and $y$, we have:

$$-3=m(6)+8$$

Solving for $m$, we find:

$$m=-\frac{11}{6}$$

And so our line is:

$$y=-\frac{11}{6}x+8$$

This agrees with your result. (Yes)
 
MarkFL said:
We are given that the line has $y$-intercept 8, so your line may be written as:

$$y=mx+8$$

Now, we are given the point on the line $(6,-3)$, and so substituting for $x$ and $y$, we have:

$$-3=m(6)+8$$

Solving for $m$, we find:

$$m=-\frac{11}{6}$$

And so our line is:

$$y=-\frac{11}{6}x+8$$

This agrees with your result. (Yes)

Always good to know more than one method. BTW, thank you for answering my PM questions. I will reply in full later today...
 
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