Couple of questions on linear geometry

[MadmanMurray]

I know the formulas for coordinate geometry of the straight line and I've done a fair bit of it but I have trouble when it comes to converting equations into lines with coordinates.

Heres an example of a question I can't answer
L is the line 2x - 3y - 7 = 0. Verify that the point a(-1,-3) is in L.

Find
i) the slope of L
ii) the coordinates of the points where L intercepts the y-axis
iii) the equation of the line parallel to L through the point (-3,0)

First off I assume that to verify (-1,-3) is on the line L I just plug those values into the equation for L. I did that and the answer comes out to 7 not 0 so I assume (-1,-3) is not on the line.

i) To find the slope I would use the formula -a/b which would give me -2/3. Another way I'd get the slope is to rearrange the equation into y = m(x) form and doing that I get the same result -2/3. Is this correct?

ii) To find the y intercept of a point I would arrange the equation into its slope intercept form and here's what I get y = -2/3(x) + 7 so in this case I'd assume the y intercept is 7 but this seems to be incorrect

iii) for this one I'd use the formula y - y1 = m(x - x1)

So the main part of this I'm having trouble with is finding the y intercept of line L because if I try to get it by letting y in the equation = 0 I get a different answer to 7.

I also don't get why they say "verify" that points on the line if it isn't even on the line. I woulda thought they'd say "find out if point (-1,-3) is on L"

 

[NoMoreExams]

I know the formulas for coordinate geometry of the straight line and I've done a fair bit of it but I have trouble when it comes to converting equations into lines with coordinates.

Heres an example of a question I can't answer
L is the line 2x - 3y - 7 = 0. Verify that the point a(-1,-3) is in L.

Find
i) the slope of L
ii) the coordinates of the points where L intercepts the y-axis
iii) the equation of the line parallel to L through the point (-3,0)

First off I assume that to verify (-1,-3) is on the line L I just plug those values into the equation for L. I did that and the answer comes out to 7 not 0 so I assume (-1,-3) is not on the line.

The equation is 2x - 3y - 7 and when you plug in (-1, -3) you don't get 0? You need to recheck your algebra.

i) To find the slope I would use the formula -a/b which would give me -2/3. Another way I'd get the slope is to rearrange the equation into y = m(x) form and doing that I get the same result -2/3. Is this correct?

ii) To find the y intercept of a point I would arrange the equation into its slope intercept form and here's what I get y = -2/3(x) + 7 so in this case I'd assume the y intercept is 7 but this seems to be incorrect

Yes you should rewrite that as y = m*x + b, m would be the slope, b would the y intercept. You have not done that .. so do that

iii) for this one I'd use the formula y - y1 = m(x - x1)

So the main part of this I'm having trouble with is finding the y intercept of line L because if I try to get it by letting y in the equation = 0 I get a different answer to 7.

I also don't get why they say "verify" that points on the line if it isn't even on the line. I woulda thought they'd say "find out if point (-1,-3) is on L"

Yes you would use the formula $$y - y_{1} = m(x-x_{1})$$, you should get m from the parts above and you are told what $$(x_{1}, y_{1})$$ is so just plug and chug.

I also don't think this belongs in Topology and Geometry... maybe homework help.