How do you write the equation in slope intercept form given (-5,0) and (3,3)?

2 Answers
Apr 12, 2017

See the entire solution process below:

Explanation:

First, we need to determine the slope for this equation. The slope can be found by using the formula: m = (color(red)(y_2) - color(blue)(y_1))/(color(red)(x_2) - color(blue)(x_1))

Where m is the slope and (color(blue)(x_1, y_1)) and (color(red)(x_2, y_2)) are the two points on the line.

Substituting the values from the points in the problem gives:

m = (color(red)(3) - color(blue)(0))/(color(red)(3) - color(blue)(-5)) = (color(red)(3) - color(blue)(0))/(color(red)(3) + color(blue)(5)) = 3/8

The slope-intercept form of a linear equation is: y = color(red)(m)x + color(blue)(b)

Where color(red)(m) is the slope and color(blue)(b) is the y-intercept value.

We can substitute the slope we calculated and one of the points from the problem for x and y and solve for b:

3 = (color(red)(3/8) xx 3) + color(blue)(b)

3 = color(red)(9/8) + color(blue)(b)

3 - 9/8 = -9/8 + color(red)(9/8) + color(blue)(b)

(3 xx 8/8) - 9/8 = 0 + color(blue)(b)

24/8 - 9/8 = color(blue)(b)

15/8 = color(blue)(b)

Substituting this result and the slope we calculated into the formula gives:

y = color(red)(3/8)x + color(blue)(15/8)

Apr 12, 2017

The equation of the line in slope-intercept form is y= 3/8 x+1 7/8

Explanation:

The slope of the line passing through (-5,0) and (3,3) is m= (y_2-y_1)/(x_2-x_1)= (3-0)/(3+5)=3/8

Let the equation of the line in slope-intercept form be y=mx+c or y=3/8x+c The point (-5,0) will satisfy the equation . So, 0= 3/8*(-5)+c or c= 15/8 = 1 7/8

Hence the equation of the line in slope-intercept form is y= 3/8 x+1 7/8 graph{3/8x+15/8 [-10, 10, -5, 5]} [Ans]