Question

A line passes through the points (2, 2) and (3, 7). What is its equation in slope-intercept form?

Write your answer using integers, proper fractions, and improper fractions in simplest form.

y =
x −

Answer 1

Answer: y = 5x - 8

Explanation:

• General equation of a line:

`{ \boxed{ \rm{y = mx + c}}}`

• m is the slope
• c is the y-intercept

`{ \rm{slope = (y _(2) - y _(1) )/(x _(2) - x _(1)) }} \\ \\ { \rm{m = (7 - 2)/(3 - 2) = (5)/(1) }} \\ \\ { \rm{m = 5}}`

• Considering point (2, 2), substitute in the equation.

`{ \rm{y = mx + b}} \\ \\ { \rm{2 = (5 * 2) + c}} \\ \\ { \rm{2 = 10 + c}} \\ \\ { \rm{c = {}^( - ) 8}}`

• Therefore, equation of a line is;

`{ \boxed{ \rm{y = 5x - 8}}}`