write an equation in point-slope form for the line that passes through (0,-2), (3,2). Then use the same set of points to write the equation in standard form and again in slope-intercept form.

Question

step by step process of finding the point-slope, standard form, and slope-intercept  of the line that passes through (0,-2), (3,2)

Answer 1

The equation is of the form y=mx+c where m is the gradient and c the intercept.

To find m we use the points: m=(difference of y values)/(difference of x values)=(2-(-2))/(3-0)=4/3.

So now we have y=4x/3+c.

Take one point and plug in x, y. Use (0,-2): -2=c so c=-2 and y=4x/3-2 is the equation in slope-intercept form. (This can be written: 3y=4x-6.) Note that (3,2) also fits.