Question

Maria wrote the equation of a line that has a slope of Four-thirds and passes through point (3, 5). Which statement is true?
1. The y-intercept is 4.
2. The slope-intercept equation is y = four-thirds x + 1.
3. The point-slope equation is y minus 3 = four-thirds (x minus 5).
4. The line also passes through the point (0, –2).

Answer 1

Given info : Maria wrote the equation of a line that has a slope of Four-thirds and passes through point (3, 5).

To find correct statement :

1. The y-intercept is 4.
2. The slope-intercept equation is y = four-thirds x + 1
3. 3. The point-slope equation is y minus 3 = four-thirds (x minus 5).
4. 4. The line also passes through the point (0, –2)

solution : slope of line = 4/3

the line passing through point (3,5)

so equation of line ,

(y - 5) = 4/3(x - 3)

⇒3(y - 5) = 4(x - 3)

⇒3y - 15 = 4x - 12

⇒4x - 3y + 3 = 0

so, y intercept : at x = 0 , y = 1

slope intercept equation of line is , y = 4/3 x + 1

Therefore the correct option is (2) the slope - intercept equation of line is y = 4/3 x + 1