Question 87565
Write the equation in slope-intercept form: {{{y = mx+b}}} for the line containing the two points (-3, 7) and (4, -7).
You can find the slope, m, by: {{{m = (y[2]-y[1])/(x[2]-x[1])}}} where: ({{{x[1]}}}, {{{y[1]}}}) = (-3, 7) and ({{{x[2]}}}, {{{y[2]}}}) = (4, -7)
{{{m = (-7-7)/(4-(-3))}}}
{{{m = -14/7}}}
{{{m = -2}}}
So now you have:
{{{y = -2x+b}}} Next, you need to find the value of the y-intercept, b.
To do this, you will substitute the x- and y-coordinate values from either one of the two given points into this equation and solve for b.
Let's choose the second point (4, -7) so we'll substitute x = 4 and y = -7 and solve for b.
{{{-7 = -2(4)+b}}} Simplify.
{{{-7 = -8+b}}} Add 8 to both sides.
{{{1 = b}}}
Now you can write the final equation in the point-slope form.
{{{y = -2x+1}}} ...and there it is!
And here's what the graph of this line would look like:
{{{graph(400,300,-5,5,-8,10,-2x+1)}}}