Question

I don't under stand this question.

Write the equation of the line that passes through (2, 4) and (1, –3) in slope-intercept form.

The answer is y = 7x – 10, but how?

Answer 1

Find the slope via \[m=\frac{y_2-y_1}{x_2-x_1}\]

Then use the formula for a line through a given point:
\[y-y_0 = m(x-x_0)\]
and rearrange as necessary.

Answer 2

You are given two points. Any two distinct points may define a line. The slope of the line is the 'rise' divided by 'run' or gradient. Plus any line extends infinitely in either direction and must intercept the y-axis somewhere : provided they are not parallel ie. the line is not 'vertical'. The general formula to satisfy here is:\[\frac{y-y_0}{x-x_0}=m\]where m is the slope, (x, y) is some general point on the line and (x0, y0) is some particular point on the line. But we have a second point! So\[\frac{4-(-3)}{2-1}= 7=m\]so we have the gradient. Now for the intercept, rearranging the above formula gives :\[y-y_0 = m(x-x_0)\]\[y= y_0 +mx - mx_0\]or is of the form\[y= mx + c\]thus far we have in this case\[y=7x+c\]which is true for all points on the line, now use either of the given points say (2,4):\[4=7\times 2+c\]\[c=4-14=-10\]and there you have the full equation. Check with the other point (1, -3) if you like\[-3=7\times 1 + c\]\[c=10\]

Answer 3

Thank you! ^~^