Question 335606
Let's start with the "slope-intercept" form of a linear equation.
y = mx+b where m is the slope and b is the y-intercept.
We can calculate the slope, m, using the two given points (30,65) and (70,95) as follows:
{{{m = (y[2]-y[1])/(x[2]-x[1])}}}
The x's and the y's here are taken from the two points.
{{{m = (95-65)/(70-30)}}}
{{{m = 30/40}}}
{{{m = 3/4}}} so now we can write...
{{{y = (3/4)x+b}}} To find the value of b, we'll use the x- and y-coordinates from either one of the two given points.  Let's use (30,65).
{{{65 = (3/4)(30)+b}}} Simplify.
{{{65 = (90/4)+b}}} Simplify the fraction.
{{{65 = (45/2)+b}}} Multiply everything by 2 to clear the fraction.
{{{130 = 45+2b}}} Subtract 45 from both sides.
{{{85 = 2b}}} divide both sides by 2.
{{{b = 42.5}}}
Now we can write the final equation in slope-intercept form:
{{{highlight(y = (3/4)x+42.5)}}}
Let's see how that looks when graphed:
{{{graph(400,400,-5,100,-5,100,(3/4)x+42.5)}}}