Question 192690
Write the equation of the line that passes through the points (3, -5) and (5, 7)
You could use the "slope-intercept" form of the equation: y = mx+b where m = slope and b = y-intercept.
To find the slope:
{{{m = (y[2]-y[1])/(x[2]-x[1])}}} Using the x- and y-coordinates of the given points, make the appropriate substitutions:
{{{m = (7-(-5))/(5-3)}}} Simplify.
{{{m = 12/2}}}
{{{m = 6}}}
So now you have:
{{{y = 6x+b}}} and you need to find b, the y-intercept. Use the x- and y-coordinates of either one of the two given points and substitute:
{{{7 = 6(5)+b}}}
{{{7 = 30+b}}} Subtract 30 from both sides.
{{{-23 = b}}}
Now you can write the final equation in slope-intercept form:
{{{highlight_green(y = 6x-23)}}}