How do you write an equation in slope intercept form given that the line passes through the points (1,5) and (0,0)?

Question

How do you write an equation in slope intercept form given that the  line passes through the points (1,5) and (0,0)?

Eva Adamson · Accepted Answer

#y = 5x + 0#

Determine the slope first.

If a line passes through two points #(x_1, y_1)# and #(x_2, y_2)# then its slope #m# is (change in #y#) / (change in #x#), given by the formula:

#m = (Delta y)/(Delta x) = (y_2 - y_1) / (x_2 - x_1)#

To avoid negative values, I will swap the order of the two points given in the question, and let #(x_1, y_1) = (0, 0)# and #(x_2, y_2) = (1, 5)#

Then:

#m = (5 - 0) / (1 - 0) = 5/1 = 5#

Therefore, the line's equation in slope-intercept form needs to be:

#y = 5x+c#

for some constant #c# - which is the #y# coordinate of the intercept with the #y# axis.

Any point on the line must satisfy this line's equation, giving us:

#y_1 = 5x_1 + c#

That is:

#0 = (5*0) + c#

So #c = 0# and the equation of the line can be written:

#y = 5x + 0#

Hazel Anglin · Answer

undefined To write an equation in slope-intercept form (y = mx + b) given two points, you first need to find the slope (m) using the formula:

m = (y2 - y1) / (x2 - x1)

Substitute the coordinates of the two points (x1, y1) and (x2, y2) into the formula to find the slope.

Once you have the slope (m), choose one of the points and substitute its coordinates into the equation. Then solve for the y-intercept (b).

Finally, write the equation using the slope and y-intercept you found.