Determine equation of line described. put in slope intercept form if possible

In summary, the conversation discusses a problem involving finding the equation of a line that passes through a given point and is perpendicular to a given line. The process involves finding the slope of the given line and using the negative reciprocal as the slope for the line in question, which can then be solved using the point-slope formula. The conversation ends with a request to rearrange the given line into slope-intercept form.
  • #1
Snicklefritz
2
0
okay so as usual I am stumped ( I am not sure if I dislike math, or simply those who proclaim to be teachers of it. Spouting off steps is not the same thing as teaching ) Anyway, I have a problem that requires me to determine the equation of the line described:

Through (6,-4), perpendicular to -7x +5y=-62

Any help is greatly appreciated.
 
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  • #2
Okay, we are given one point on the line, and we are told this line is perpendicular to the line:

\(\displaystyle -7x +5y=-62\)

We need to find the slope of this line, so that we may use the negative reciprocal of this slope as the slope of the line we are asked to find. This way we will have a point and the slope, and then we can apply the point-slope formula to obtain the equation of the line in question.

So, can you arrange the given line in slope-intercept form:

\(\displaystyle y=mx+b\) ?
 

Related to Determine equation of line described. put in slope intercept form if possible

1. What is the slope-intercept form of a line?

The slope-intercept form of a line is y = mx + b, where m represents the slope of the line and b represents the y-intercept, or the point where the line crosses the y-axis.

2. How do you determine the slope of a line?

The slope of a line can be determined by calculating the change in y-coordinates over the change in x-coordinates between any two points on the line. This can be expressed as (y2 - y1) / (x2 - x1).

3. Can you determine the equation of a line if you only have one point and the slope?

Yes, it is possible to determine the equation of a line with just one point and the slope. You can use the point-slope form of a line, which is y - y1 = m(x - x1), where (x1, y1) is the given point and m is the given slope.

4. How do you convert a line from standard form to slope-intercept form?

To convert a line from standard form (Ax + By = C) to slope-intercept form, you can solve for y by subtracting Ax from both sides and then dividing by B. This will give you the equation in the form y = (-A/B)x + (C/B).

5. Is it possible for a line to have a negative slope-intercept form?

Yes, it is possible for a line to have a negative slope-intercept form. This means that the line has a negative slope, which indicates that it is decreasing as it moves from left to right on a graph. The y-intercept can also be negative in this case.

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