What is the equation of each line in slope-point form? 10 pts?

Question

same x-intercept as the line y= 3x - 4 and through (0,5)
and what about if the question is x-intercept of -5 and y-intercept of 4?
 

Answer 1

Slope - intercept form line equation is y = mx + b, where m is slope and b is y-intercept.

1.

same x-intercept as the line y= 3x - 4 and through (0,5)

Find x-imtercept by substituting y  = 0 in equation.

0 = 3x - 4

x = 4/3, The coordinate is (4/3 , 0)

Now find the slope m = (y2 - y1) / (x 2 - x1)

m = (0 - 5) / (4/3 - 0) = -15/4

The line equation is y = -15/4x + b

Find y-intercept value by substituing  (0, 5 ) in the equation

5 = -15/4 * 0 + b

b = 5

The line equation is y = -15/4 x + 5 or 15x + 4y = 20

Answer 2

2.

x-intercept is -5, so line passing through point (-5, 0)

y-intercept is 4, so line passing through point (0, 4)

Now find the slope m = (y2 - y1) / (x 2 - x1)

m = (0 -4) / (-5 - 0) = 4/5

The line equation is y = 4/5x + b

Find y-intercept value by substituing  (0, 4) in the equation

4 = 4/5 * 0 + b

b = 4

The line equation is y = 4/5x + 4