If the slope of a line and a point on the line are known, the equation of the line can be found using the slope-intercept form, ymxb. To do so, substitute the value of the slope and the values of x and y using the coordinates of the given point, then determine the value of b. Using the above technique, find the equation of the line containing the points (-3,19) and (6,-2)

2y + 3x = 3

Step-by-step explanation:

The standard form of equation of a line is expressed as;

y = mx+c

m is the slope

b is the intercept

We are to find the equation of a line passing through the points  (-3,19) and (6,-2)

First get the slope

m = y2-y1/x2-x1

m = -2-19/6-(-3)

m = -21/9

m = -7/3

Get the y- intercept b;

Substitute the coordinate (6, -2) and m = -7/3 into the expression y = mx+b and get b;

-2 = -7/3(6) + c

-2 = -7/2 + c

c = 7/2 - 2

c = (7-4)/2

c = 3/2

Substitute the slope and intercept into the formula

y = mx+b

y = -7x/2 + 3/2

Multiply through by 2;

2y = -7x + 3

2y + 7x = 3

Hence the required equation is 2y + 7x = 3