Question 1204563
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The responses from both of the other tutors say to plug numbers into a formula that gives you the equation of a line passing through two given points.<br>
If you are in a job where you have to do that 50 times a day, then having a formula to plug numbers into is useful.<br>
But plugging numbers into a formula doesn't teach you much.  And what if you are a beginning student and are not familiar with the formula and accidentally plug the numbers in the wrong places?<br>
Assuming you are a student just starting to learn algebra, it is best if you work the problem using basic ideas.<br>
To find the slope of the line, I strongly recommend using "rise over run" with a mental (or paper and pencil) sketch of the given points -- instead of using the ubiquitous formula for calculating the slope.<br>
The run (change in x) is 6, from -2 to 4; the rise is 8, from -3 to 5.  So the slope "rise over run" is 8/6 or 4/3.<br>
Then I think the most instructional way to find the equation is to use the slope-intercept form of the equation with one of the given points to find the intercept.  Using (x,y)=(4,5):<br>
{{{y=mx+b}}}
{{{5=(4/3)(4)+b}}}
{{{5=16/3+b}}}
{{{b=-1/3}}}<br>
One form of the equation is then<br>
{{{y=(4/3)x-1/3}}}<br>
You can of course write the equation in equivalent forms.  Multiplying by 3 to clear the fractions...<br>
{{{3y=4x-1}}}
{{{4x-3y-1=0}}}
{{{4x-3y=1}}}<br>