Question 105896
Write the equation, in slope-intercept form, of the line that passes through the points (7, 6) and (1, -12)
You can find the slope, m, of the line using:
{{{m = (y[2]-y[1])/(x[2]-x[1])}}} where: {{{x[1] = 7}}}, {{{y[1] = 6}}}, {{{x[2] = 1}}}, and {{{y[2] = -12}}}
{{{m = (-12-6)/(1-7)}}}
{{{m = (-18)/(-6)}}}
{{{m = 3}}}
Now you can start the equation as:
{{{y = mx+b}}} Replace the m with the slope just calculated: m = 3
{{{y = 3x+b}}} Now we need to find the value of b. You can do this by substituting into this equation, the x- and y-coordinates of either one of the two given points. Let's use the first point (7, 6)
{{{y = 3x+b}}} Substitute x = 7 and y = 6
{{{6 = 3(7)+b}}} Simplify and solve for b.
{{{6 = 21+b}}} Subtract 21 from both sides.
{{{-15 = b}}} Now you can write the final equation:
{{{y = 3x-15}}}