Question

1 ) Write the equation of a line passing through the points (-5, 8) and (-4, 4) in slope-Intercept form.

Answer 1

Question:

Write the equation of a line passing through the points (-5, 8) and (-4, 4) in slope-Intercept form.​

Solution:

The slope-intercept form of the line is given by the equation:

y = mx +b

where m is the slope of the line and b is the y-coordinate of the y-intercept (when x=0). Now, by definition the slope of the line is given by the following equation:

`m\text{ = }(Y2-Y1)/(X2-X1)`

where (X1,Y1) and (X2,Y2) are points on the line. In this case, we have that

(X1, Y1) = (-5,8)

(X2,Y2) = (-4,4)

then, replacing these values in the equation of the slope we obtain:

`m\text{ = }(Y2-Y1)/(X2-X1)=\text{ }(4-8)/(-4-(-5))=\text{ }(-4)/(-4+5)=(-4)/(1)=\text{ -4}`

Thus, the equation of this line would be:

y = -4x +b

now, to find b, replace any point (x,y) in the above equation and solve for b. For example, take (x,y) = (-5,8). Then, we have:

8 = -4(-5) + b

this is equivalent to

8 = 20 + b

solve for b:

b = 8-20 = -12

thus, we can conclude that the equation in slope-intercept form of the given line is:

`y\text{ = -4x -12}`